Answer:
The mean of the the random variable X is 1200.
The standard deviation of the random variable X is 21.91.
Step-by-step explanation:
The random variable X is defined as the number of city residents in the sample who support the proposal.
The random variable X follows a Binomial distribution with parameters n = 2000 and p = 0.60.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10Check the conditions as follows:
[tex]np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, the random variable X can be approximate by the Normal distribution .
Compute the mean of X as follows:
[tex]\mu=np[/tex]
[tex]=2000\times 0.60\\=1200[/tex]
The mean of the the random variable X is 1200.
Compute the standard deviation of X as follows:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91[/tex]
The standard deviation of the random variable X is 21.91.
!Please solve and help!!!! I don't know what it is!!
Answer:
see below
Step-by-step explanation:
This problem could have 2 solutions
We could be given two legs
a^2 + b^2 = c^2
5^2 +13^2 = c^2
25+169 = c^2
194 = c^2
Taking the square root on each side
sqrt(194) = c
Or the 13 could be the hypotenuse
a^2 + 5^2 = 13^2
a^2 +25 = 169
a^2+25-25 = 169-25
a^2 = 144
Taking the square root of each side
a = 12
Multiply the fractions and reduce to lowest terms: 16 x 5/9 x 2 1/2
Answer:
thee answer is 22.22 hopes this helps
To multiply fractions 16, 5/9, and 2 1/2 and reduce to lowest terms, convert mixed numbers to improper fractions, multiply the numerators and denominators, and then simplify by common factors. The reduced answer is 200/9.
To multiply the fractions and reduce to lowest terms of the expression 16 x 5/9 x 2 1/2, we first convert the mixed number to an improper fraction. The number 2 1/2 can be written as 5/2 because 2 x 2 + 1 = 5.
Now, we have the multiplication of three numbers, which is 16 x 5/9 x 5/2. Multiplying the numerators together and the denominators together, we get 16 x 5 x 5 in the numerator and 1 x 9 x 2 in the denominator, simplifying to 400/18.
To reduce this fraction to the lowest terms, we divide the numerator and the denominator by the greatest common divisor, which is 2. This gives us 200/9. The final answer cannot be reduced further, so the reduced fraction is 200/9.
Which statement is correct regarding the measurements of the parallelogram?
On a coordinate plane, a parallelogram has points (16, 4), (10, 1), (2, 1), (8, 4).
The base is 6 and the height is 3, so the area is 6 (3) = 18 square units.
The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.
The base is 8 and the height is 4, so the area is 8 (4) = 32 square units.
The base is 8 and the height is 6, so the area is 8 (6) = 48 square units.
Answer:
The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.
Step-by-step explanation:
The area of the parallelogram is given by the following expression:
[tex]A = \|\vec u\times \vec v\|[/tex]
The vectors are, respectively:
[tex]\vec u = (10-2, 1 - 1,0-0)[/tex]
[tex]\vec u = (8,0,0)[/tex]
The base of the parallelogram is 8 units.
[tex]\vec v = (8-2, 4-1,0-0)[/tex]
[tex]\vec v = (6,3,0)[/tex]
The height of the parallelogram is 3 units.
The cross product of both vectors is:
[tex]\vec u \times \vec v = (0,0,24)[/tex]
The area of the parallelogram is given by the norm of the resulting vector:
[tex]\|\vec u \times \vec v\| = 24[/tex]
Answer:
B. The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.The equation of a circle is x2 + 8x + y2 - 12y = 144. What are the coordinates of the center and the length of the radius of the circle?
Answer:
The centre is the point (-4,6).
The length of the radius is 14.
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius and the centre is the point [tex](x_{0}, y_{0})[/tex]
In this question:
We have to complete the squares, to place the equation in the general format:
So
[tex]x^{2} + 8x + y^{2} - 12y = 144[/tex]
To complete the quares, we divide each first order term(8 and -12) by two, having two new terms(4 and -6). With this, we write as the square of (x+4) and (y-6). To compensate, we have to find the square of 4 and -6 on the other side of the equality.
[tex](x+4)^{2} + (y-6)^{2} = 144 + (4)^{2} + (-6)^{2}[/tex]
[tex](x+4)^{2} + (y-6)^{2} = 196[/tex]
The centre is the point (-4,6).
The length of the radius is [tex]\sqrt{196} = 14[/tex]
The center and the length of the radius of the circle is (-4, 6) and 14units respectively
Equation of a circleThe standard equation of a circle is expressed as:
x^2+y^2+2gx+2fy+c = 0
where:
C = (-g, -f)
r = √g²+f²-c
Given the equation of a circle expressed as:
x^2 + 8x + y^2 - 12y = 144.
Compare both equations
2gx = 8x
g = 4
2fy = -12y
y = -6
The centre of the circle will be at (-4, 6)
Determine the radius
r = √4²+6²+144
r = 14
Hence the center and the length of the radius of the circle is (-4, 6) and 14units respectively
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find the center and the radius of the circle with the equation x^2 -2x+y^2 +4y +1
Answer:
Center = ( 1,-2)
radius = 2
Answer:
^D
Step-by-step explanation:
Help! Best answer = Brainiest.
Answer:
Step 2
Step-by-step explanation:
La escuela se encuentra en un terreno rectangular y está próximo a adquirir uno más de forma rectangular. Este último equivale a 1/4 del tamaño actual de la escuela. Si la escuela mide 50 metros de largo y 12 de ancho. Cada salón de la escuela ocupa 1/16 del terreno acutual cuántos salones se podrían construir en el terreno nuevo.?
El patio de la escuela equivale a 3 /5 del terreno. Cuantos salones en un primer piso tiene aproximadamente un la escuela.
Si se quiesiera agregar únicamente 2 salones más y una cancha de fútbol de 3/4 del terreno original que te tanto más de espacio se necesitaría en el nuevo terreno.?
Answer:
- 4 new classrooms can be built on the newly acquired plot.
- The number of classrooms on the first floor of the school's land = 8
- The amount of extra space on the new land needed to add just 2 more rooms and a soccer field 3/4 of the original land = 375 m²
Step-by-step explanation:
The current rectangular plot for the school has dimensions 50 m length and 12 m width.
The current school plot has an area of (50×12) that is, 600 m².
The newly acquired rectangular plot, is said to be (1/4) of the current plot.
Area of the newly acquired rectangular plot
= (1/4) × 600 = 150 m²
Each classroom on the current school's plot occupies (1/16) of the the current rectangular plot, area of a classroom on the current plot.
= (1/16) × 600 = 37.5 m²
So, how many classrooms can be obtained from the newly acquired rectangular plot?
Area of the newly acquired rectangular plot = 150 m²
Area of one classroom = 37.5 m²
Number of classrooms obtainable from the newly acquired rectangular plot = (150/37.5)
= 4 classrooms
b) The schoolyard is equal to 3/5 of the land. How many classrooms on the first floor does the school have?
Total area of school land now = 600 m² + 150 m² = 750 m²
Schoolyard occupies (3/5) of the space.
Then, the classrooms on the first floor will occupy (2/5) of the space.
Area occupied by classrooms = (2/5) × 750
= 300 m²
Recall, each classroom occupies 37.5 m² of space,
Hence, the number of classrooms on the first floor = (300/37.5) = 8 classrooms to the nearest whole number.
c) If you wanted to add just 2 more rooms and a soccer field 3/4 of the original land, so much more space would be needed in the new field?
2 more classrooms will occupy = 2 × 37.5 = 75 m²
(3/4) of the original land = (3/4) × 600 = 450 m²
Total new space required = 75 + 450 = 525 m²
The newly acquired rectangular plot has an area of 150 m², So, to achieve those two projects (add just 2 more rooms and a soccer field 3/4 of the original land) that would require 525 m².
The amount of extra space that will be required = 525 - 150 = 375 m²
Hope this Helps!!!
Major Motors produces its Trans National model in three plants located in Flint, Michigan; Fresno, California; and Monterrey, Mexico. Dealers receive cars from regional distribution centers located in Phoenix, Arizona; Davenport, Iowa; and Columbia, South Carolina. Anticipated production at the plants over the next month (in 100s of cars) is 43 at Flint, 26 at Fresno, and 31 at Monterrey. Based on firm orders and other requests from dealers, Major Motors has decided that it needs to have the following numbers of cars at the regional distribution centers at month’s end: Phoenix, 26; Davenport, 28; and Columbia, 30. Suppose that the cost of shipping 100 cars from each plant to each distribution center is given in the following matrix (in $1,000s):
From To
Phonix Devenport Columbia
Flint 12 8 7
Fresno 7 14 21
Monterrey 18 22 31
Convert the above problem into a balanced one by adding a row or column and compute the solution provided by the Greedy Heuristic.
Answer:
See attached image for a balanced one by adding a row
Final answer:
The question involves converting an unbalanced transportation problem for Major Motors into a balanced one and solving it using the Greedy Heuristic. It requires adding a dummy destination with zero shipping cost and then allocating the supply to demand sites starting from the lowest shipping costs.
Explanation:
The student's question pertains to creating a balanced transportation problem from the given unbalanced scenario involving Major Motors and using the Greedy Heuristic to find a solution. The three plants located in Flint, Fresno, and Monterrey have production capacities of 43, 26, and 31 (in hundreds of cars) respectively, and the distribution centers in Phoenix, Davenport, and Columbia have requirements of 26, 28, and 30 (in hundreds of cars) respectively.
First, we need to balance the problem by equating total supply with total demand. The total supply from all plants is 43 + 26 + 31 = 100 (in hundreds of cars), and the total demand from all distribution centers is 26 + 28 + 30 = 84 (in hundreds of cars). We will need to add a dummy distribution center with a demand of 16 (in hundreds of cars) to balance the problem, with zero shipping cost to this dummy destination from all plants. Now, we apply the Greedy Heuristic, which involves selecting the lowest cost choices first and fulfilling demand as supply allows.
We start by assigning cars to the distribution centers from the cheapest shipping options available. Let's illustrate a step, shipping from Flint to Columbia as it has the lowest cost of $7,000 for 100 cars. Continuing this process until all demands are met will provide us with an approximate solution to the transportation problem.
HELP NOW PLEASE !!!Mrs. Havarti's art class made five identical conical sculptures. Each sculpture has a diameter of 9 cm and a slant height of
16.5 cm. The lateral area of each sculpture is to be covered with newspaper. How many square centimeters of newspaper are
needed to cover the lateral areas of all five sculptures? (Use 3.14 for x and round to the nearest hundredth. Recall the formula
LA- rl.)
233.15 cm
466.29 cm
1,165.73 cm
2,331.45 cm
Answer:
1165.73 sq.cm. of newspaper are needed to cover the lateral areas of all five sculptures
Step-by-step explanation:
Diameter of 1 sculpture = 9 cm
Radius of 1 sculpture =[tex]\frac{9}{2}=4.5 cm[/tex]
Slant height of sculpture = l = 16.5 cm
Lateral surface area of each sculpture = [tex]\pi r l = \frac{22}{7} \times 4.5 \times 16.5 =233.3571 cm^2[/tex]
Lateral surface area of 5 sculptures =[tex]233.3571 \times 5 =1165.73 cm^2[/tex]
Hence 1165.73 sq.cm. of newspaper are needed to cover the lateral areas of all five sculptures
Answer:
1,165.73 cm^2
Step-by-step explanation:
There is a group of 15 people ordering pizza. If each person gets 2 slices and each pizza has 15 slices. How many pizzas should they get
Answer:
2 pizza's
Step-by-step explanation:
15x2=30
30 divided by 2 equals 15
the amount of pizza required is 30
there are a group of 15 people
each of these person gets 2 slices of pizza
each pizza has 15 slices
therefore the number of pizza needed is
= 2 × 15
= 30
Hence 30 pizzas are needed for the group of 15 people
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The score on a geometry test are normally distributed with a mean of 80 and a standard deviation of 5, the test scores range from 0 to a 100, 12 students had test scores between 80 and 90. Estimate the number of students who took the test.
Final answer:
To estimate the number of students who took a geometry test based on certain scores and parameters, consider the range of scores and standard deviations to make the calculation.
Explanation:
The question:
The student is asking to estimate the number of students who took a geometry test given certain scores and parameters.
Step-by-step explanation:
Given that 12 students scored between 80 and 90 on the test, we know this range corresponds to 1 standard deviation above the mean of 80.Since the standard deviation is 5, and the range from 80 to 90 covers 1 standard deviation, the total number of students can be estimated by calculating how many standard deviations cover the full range of scores from 0 to 100.Dividing the total range of 100 by the width of one standard deviation (5) gives us an estimate of 20 standard deviations in total, and therefore, an estimate of 20 students who took the test.HELP ASAP.....Researchers are conducting a survey about what brand of ice cream shoppers prefer. They survey the tenth person who walks into the store and then every fifth person after that. This type of sampling is called
a)random sampling.
b)stratified sampling.
c)systematic random sampling.
d)cluster sampling.
HURRY!!!!
Answer:
c.systematic random sampling.
Step-by-step explanation:
Using sampling concepts, it is found that this type of sample is called systematic random sampling, which means that option c is correct.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, after the 1st person is surveyed, every kth person, with k = 5 is surveyed, hence it is a systematic random sampling and option c is correct.
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Write the following expression as a single logarithm with coefficient 1. log910 − log9 1 2 − log94
The answer is A. Log 9 5
I got it right on ed .
The value of the expression log₉10-log₉(1/2)-log₉4 is log₉5.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is
log₉10-log₉(1/2)-log₉4
if we observe the base of logs are same
so, we can use property of logarithms
[tex]log_{a} b+log_{a} c=log_{a} bc[/tex]
log₉10-log₉(1/2×4)
Now we use the property of logarithms of subtraction.
log₉10-log₉(2)
log₉(10/2)
log₉5
Hence, the value of the expression log₉10-log₉(1/2)-log₉4 is log₉5.
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Solve this equation 3/5(x-10)=18-4x-1 combine like terms that are on the same side of the equation
Answer:
x=5
Step-by-step explanation:
3/5(x-10)=18-4x-1
3/5x-30/5=18-4x-1
3/5x-6=18-4x-1
+6 +6
3/5x=23-4x
+4x +4x
4 3/5x=23
23/5x=23
23/5 divide , so you actually multiply both sides by the reciprocal 5/23
x=5
The solution of equation will be : x=5
Given,
3/5(x-10)=18-4x-1
Here,
Multiply 3/5 inside the bracket,
3/5(x-10)=18-4x-1
3/5x-30/5=18-4x-1
3/5x-6=18-4x-1
Now solve like terms individually.
3/5x=23-4x
4x + 3/5x=23
23/5x=23
x=5
Thus the value of x is 5 .
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If the ratio between the radii of the two spheres is 3:5, what is the ratio of
their volumes?
The Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several lakes in your water district. A total of 15 devices will be used. Assume that each device has a probability of 0.05 of failure during the course of the monitoring period. What is the probability that one of the devices fail?
Answer:
36.58% probability that one of the devices fail
Step-by-step explanation:
For each device, there are only two possible outcomes. Either it fails, or it does not fail. The probability of a device failling is independent of other devices. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A total of 15 devices will be used.
This means that [tex]n = 15[/tex]
Assume that each device has a probability of 0.05 of failure during the course of the monitoring period.
This means that [tex]p = 0.05[/tex]
What is the probability that one of the devices fail?
This is [tex]P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{15,1}.(0.05)^{1}.(0.95)^{14} = 0.3658[/tex]
36.58% probability that one of the devices fail
The amount of time people wait in the drive through line at an In-n-Out restaurant follows a normal distribution with a mean of 138 seconds and a standard deviation of 29 seconds. What is the minimum number of seconds we could expect the longest 20% of customers to wait in line? i. Which of the following illustrates the shaded area under the normal distribution for the top 20%? a. b. ii. What is the minimum number of seconds we could expect the longest 20% of customers to wait in line? (round time to the nearest second)
Answer:
i) The sketch of the area under the normal distribution curve is attached to this solution of the question.
ii) The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162 seconds.
Step-by-step explanation:
This is is a normal distribution problem with
Mean = μ = 138 seconds
Standard deviation = σ = 29 seconds
i) Which of the following illustrates the shaded area under the normal distribution for the top 20%?
We first obtain the z-score that corresponds to the lower limit of the top 20% of the distribution of waiting times.
Let that z-score be z'
P(z > z') = 0.20
P(z > z') = 1 - P(z ≤ z') = 0.20
P(z ≤ z') = 1 - 0.20 = 0.80
P(z ≤ z') = 0.80
So, checking the normal distribution table,
z' = 0.842
we can then go ahead and obtain the waiting time that corresponds to this z-score.
Let the waiting time that corresponds to this z-score be x'
z' = (x' - μ)/σ
0.842 = (x' - 138)/29
x' = 162.42 seconds
Since, the options for the shaded area under the normal curve isn't presented with this question, the graph of the shaded area under the normal curve that corresponds to the top 20% waiting times is attached to this solution.
ii) What is the minimum number of seconds we could expect the longest 20% of customers to wait in line?
The minimum number of seconds we could expect the longest 20% of customers to wait in line corresponds to the lower limit of the top 20% waiting times obtained in (i) above.
The minimum number of seconds we could expect the longest 20% of customers to wait in line = 162.42 seconds = 162 seconds to the nearest second
Hope this Helps!!!
The function g(x) is graphed on the coordinate grid. Which statements are true of g(x)? Select three options.
A. The function g(x) is a translation of f(x) = /sqrt x.
B. The function g(x) has a domain of {x | x > –2}.
C. The function g(x) has a range of {y | y > –1}.
D. The function g(x) is represented by the function g(x) = /sqrt x - 3 - 1.
E. The function g(x) can be translated right 3 units and up 1 unit to create the function f(x) = /sqrt x.
Answer:
A. The function g(x) is a translation of f(x) = √x.C. The function g(x) has a range of {y | y > –1}.E. The function g(x) can be translated right 3 units and up 1 unit to create the function f(x) = √xExplanation:
The function f(x) = √x has been translated 3 units to the left and 1 unit down to make g(x). That means translating g(x) 3 units right and 1 unit up will make f(x). (matches choices A and E)
__
The range of the function is the vertical extent, all y-values ≥ -1. (matches choice C)
__
The translated function is ...
g(x) = f(x+3) -1 = √(x +3) -1 . . . . . does not match choice D
__
The domain of the function is the horizontal extent, all x-values ≥ -3. (does not match choice B)
Answer: A, C, E
Step-by-step explanation:
Had to do this Q on test
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
x= -4- and x = -4+
x=4 - 125 and x = 4+ / 25
x=-4-1 and x = 4+
• x= -4- and x = -4+
The zeros of the quadratic function f(x) = 2x² + 16x - 9 are obtained by using the quadratic formula, resulting in x = -4 + √{82} and x = -4 - √{82}.
To find the zeros of the quadratic function f(x) = 2x² + 16x - 9, we can either factor the quadratic, complete the square, or use the quadratic formula. The function provided is already in the standard form of a quadratic equation, ax² + bx + c = 0. For this equation, a = 2, b = 16, and c = -9.
To use the quadratic formula, x = (-b√{b² - 4ac}) / (2a), we substitute the values of a, b, and c into the formula:
x = (-(16) √{(16)² - 4(2)(-9)}) / (2(2))
x = (-16 √{256 + 72}) / 4
x = (-16 √{328}) / 4
x = (-16 √{82}) / 4
x = -4 √{82}
Therefore, the zeros of the function are x = -4 + √{82} and x = -4 - √{82}.
simplify the expression. 18+12x.
To simplify the expression 18 + 12x, combine the constant term 18 and the variable term 12x.
Explanation:To simplify the expression 18 + 12x, we combine like terms. The term 18 is a constant term and does not have any variables. The term 12x is a product of the coefficient 12 and the variable x.
Here, 18 is a constant term (a term with no variable), and 12x is a term with the variable x. Since the constant term and the x term are not like terms, they can't be combined.
So, the simplified expression is 18 + 12x.
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Using the slot method and multiple cases, calculate the probability that you would roll 3 sixes.
Answer:
P = 1/216
the probability that you would roll 3 sixes is 1/216
Step-by-step explanation:
For a given dice, there are six possibilities.
We have;
1,2,3,4,5,6
The probability of rolling a six(6) is;
P(6) = 1/6
Then, the probability of rolling 3 sixes is a multiple of the P(6), given as;
P = P(6) × P(6) × P(6)
P = 1/6 × 1/6 × 1/6
P = 1/216
the probability that you would roll 3 sixes is 1/216
The probability of getting 3 sixes in 4 dice rolls is A. [tex]\( \frac{5}{216} \)[/tex].
To find the probability of rolling exactly 3 sixes with 4 dice rolls using the slot method, we'll analyze several cases:
Step 1 :
Case 1: Three sixes in the first three rolls, any number on the fourth roll.
Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]
Case 2: Two sixes in the first two rolls, one six on the third roll, any number on the fourth roll.
Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]
Case 3: One six in the first roll, two sixes in the next two rolls, any number on the fourth roll.
Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} \).[/tex]
Case 4: One six in the last roll, three sixes in the first three rolls.
Probability for this case: [tex]\( \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \).[/tex]
Step 2 :
Now, sum the probabilities from all cases:
Total probability [tex]\(= \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{5}{6} + \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} \).[/tex]
This simplifies to [tex]\( \frac{15}{216} + \frac{1}{216} = \frac{16}{216} = \frac{2}{27} \).[/tex]
Thus, the correct option is A. [tex]\( \frac{5}{216} \), as \( \frac{2}{27} \)[/tex] is equivalent to [tex]\( \frac{5}{216} \)[/tex].
Complete Question :
Question:
Using the slot method and considering multiple cases, calculate the probability of rolling exactly 3 sixes with 4 dice rolls.
A. [tex]\( \frac{5}{216} \)[/tex]
B. [tex]\( \frac{25}{216} \)[/tex]
C. [tex]\( \frac{45}{216} \)[/tex]
D. [tex]\( \frac{125}{1296} \)[/tex]
Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a normal distribution with unknown population mean and known standard deviation 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for population mean is 512.00 ± 25.75." The confidence level for this interval is
Answer:
[tex] 25.75 = z_{\alpha/2} \frac{100}{\sqrt{100}}[/tex]
And solving for the critical value we got:
[tex] z_{\alpha/2}= \frac{25.75*10}{100} = 2.575[/tex]
Now we need to find the confidence level and for this case we can use find this probability:
[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)[/tex]
And using the normal standard distribution or excel we got:
[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)= 0.9950-0.0050= 0.99[/tex]
So then the confidence interval for this case is 99%
Step-by-step explanation:
For this case the random variable X is the scores for the SAT math scores and we know that the distribution for X is normal:
[tex] X\sim N(\mu , \sigma =100)[/tex]
They select a random sample of n =100 and they construc a confidence interval for the true population mean of interest and they got:
[tex]512.00 \pm 25.75[/tex]
for this problem we need know that the confidence interval for the true mean when the deviation is known is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is given by:
[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
And the margin of error for this interval is [tex] ME = 25.75[/tex] then we can solve for the critical value in order to find the confidence level:
[tex] 25.75 = z_{\alpha/2} \frac{100}{\sqrt{100}}[/tex]
And solving for the critical value we got:
[tex] z_{\alpha/2}= \frac{25.75*10}{100} = 2.575[/tex]
Now we need to find the confidence level and for this case we can use find this probability:
[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)[/tex]
And using the normal standard distribution or excel we got:
[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)= 0.9950-0.0050= 0.99[/tex]
So then the confidence interval for this case is 99%
Direct Mailing Company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid. A recently taken sample of 150 orders showed that 115 of them were mailed within 72 hours. What are the decision and conclusion of test? Use α=2.5%.
Answer:
We conclude that less than 90% of all orders are mailed within 72 hours after they are received.
Step-by-step explanation:
We are given that the company claims that at least 90% of all orders are mailed within 72 hours after they are received.
A recently taken sample of 150 orders showed that 115 of them were mailed within 72 hours.
Let p = proportion of orders that are mailed within 72 hours after they are received.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 90% {means that at least 90% of all orders are mailed within 72 hours after they are received}
Alternate Hypothesis, [tex]H_A[/tex] : p < 90% {means that less than 90% of all orders are mailed within 72 hours after they are received}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of orders that were mailed within 72 hours = [tex]\frac{115}{150}[/tex] = 0.767
n = sample of orders = 150
So, test statistics = [tex]\frac{0.767-0.90}{\sqrt{\frac{0.767(1-0.767)}{150} } }[/tex]
= -3.853
The value of z test statistics is -3.853.
Now, at 2.5% significance level the z table gives critical value of -1.96 for left-tailed test. Since our test statistics is less than the critical values of z as -3.853 < -1.96, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that less than 90% of all orders are mailed within 72 hours after they are received.
Which expression entered into a graphing calculator will return the probability
that 350 or fewer heads come up when flipping a coin 500 times?
Using the a TI-84 calculator, the expression is:
binomcdf(500, 0.5, 350)
The probability of having a or fewer successes, in n binomial trials, each with a p probability of successes is found according to the following expression:
binomcdf(n,p,a)
In this problem:
Fair coin, hence [tex]p = 0.5[/tex]The coin is flipped 500 times, hence [tex]n = 500[/tex]350 or fewer heads, hence [tex]a = 350[/tex]Then, the expression is:
binomcdf(500, 0.5, 350)
A similar problem is given at https://brainly.com/question/2912622
the light from the moon in lux on the night of t^th dat of 2016 is
L(t)= .25-sin (2pi(t-2)/28.5)
What is the period of the light from the moon?
Answer:28.5
Step-by-step explanation:
Noah gathered data at his school among 7th and 8th graders to see if there was an association between grade level and handedness. This table shows his data, but the number of right -handed 8th graders is missing .
Noah found there was no evidence of an association between grade level and handedness. Which of these could be the number of right-handed graders?
1)33
2)85
3)107
4)157
Answer: 4) 157
Step-by-step explanation:
We know that there is no association between the grade level and the andedness, then we should find that the ratio between left handeds and right handed is the same for both grades.
In 7-th grade we have:
Left handed : 11
Right handed: 72
The ratio is 11/72 = 0.14
Then, the ratio for the 8-th graders must be about the same:
Left handed: 24
Right handed: X
Ratio: 24/X
Let's start with the bigger option, X = 157.
24/157 = 0.15
Ok, we now see that with the bigger option we obtained almost the same ratio (if we use the smaller values for X, we will get a ratio bigger than 0.15, so 0.15 is the better aproximation that we can find to the 0.14 of the 7-th graders)
Then the correct option is 4) 157
The number of right-handed graders should be option 4.
Calculation of the number of right-handed graders:
Since in 7th grade
We have
Left-handed: 11
Right-handed: 72
So, The ratio is = 11: 72 = 0.14
Now the ratio for the 8th grade should be the same
So,
Left-handed: 24
Right-handed: X
so,
Ratio: 24/X
Now
if we can do
[tex]24\div 157 = 0.15[/tex]
0.15 = 0.15
Therefore, the option 4 is correct.
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Maria took a history test with 25 questions on it.
She correctly answered 22 questions.
Write her test score as a percent
Maria's test score is calculated by dividing the number of correct answers (22) by the total number of questions (25) and then multiplying by 100, resulting in a score of 88%.
Explanation:Maria took a history test with 25 questions and correctly answered 22 questions. To find her test score as a percent, you divide the number of correct answers by the total number of questions and then multiply the result by 100. So, Maria's score would be (22 correct answers / 25 total questions) × 100 = 88%.
This is how it calculates:
First, write the number of correct answers over the total number of questions as a fraction: 22/25.
Then, convert this fraction to a decimal by dividing 22 by 25, which equals 0.88.
Finally, multiply the decimal by 100 to get the percentage. So, 0.88 × 100 equals 88%.
Maria's test score expressed as a percent is 88%.
A park has an area of 12.5 sq miles and a width of 5 miles. What is the perimeter of the park?
Answer:
15
Step-by-step explanation:
12.5/5=2.5
2(2.5)+2*5=
5+10=15
Final answer:
To calculate the perimeter of the park with an area of 12.5 sq miles and a width of 5 miles, you divide the area by the width to get the length and then apply the formula P = 2(l + w). The perimeter of the park is 15 miles.
Explanation:
The question pertains to finding the perimeter of a park given its area and width. To find the perimeter, we need to know both the length and the width of the park. Since the area of the park is 12.5 sq miles and the width is 5 miles, we can find the length by dividing the area by the width, which gives us a length of 2.5 miles. Once we have both dimensions, we can use the formula for perimeter P = 2(l + w), where l is the length and w is the width.
Using the formula, the perimeter P = 2(2.5 miles + 5 miles) = 2(7.5 miles) = 15 miles. So, the perimeter of the park is 15 miles.
Which point is a solution to the linear inequality y < Negative one-halfx + 2? (2, 3) (2, 1) (3, –2) (–1, 3)
Answer: according to my calculations the answer is (3,-2) if im wrong im sorry but thats what i got
Step-by-step explanation:
The solution in the attached below that is point (2, 1).
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.
we have given that the linear inequality y < Negative one-half + 2
y < - 1x/2 + 2
The solution of the inequality is the shaded area below the dashed line;
y = - 1x/2 + 2
The slope of the dashed line is negative 1/2.
The y-intercept of the dashed line is the point (0,2) and the x-intercept of the dashed line is the point (4,0).
The solution is attached below.
Noted that Any point that lies on the shaded area is a solution to the inequality and if a point is a solution to the linear inequality, then the point must satisfy the inequality.
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Please answer quick plz be correct will give brainliest
Which data set does this stem-and-leaf plot represent?
{40, 88, 82, 46, 56, 60, 17, 60, 27, 17}
{7, 0, 6, 2, 8}
{77, 7, 0, 6, 6, 0, 0, 2, 8}
{17, 27, 40, 46, 56, 60, 82, 88}
A stem-and-leaf plot with a stem value of 1 with a leaf value of 7, 7, a stem value of 2 with a leaf value of 7, a stem value of 3, a stem value of 4 with a leaf value of 0, 6, a stem value of 5 with a leaf value of 6, a stem value of 6 with a leaf value of 0, 0, a stem value of 7, and a stem value of 8 with a leaf value of 2, 8.
Key: 1|7 means 17
Answer:
Answer 2 is right, you welcome :)
Step-by-step explanation:
The stem-and-leaf plot corresponds to the data set {17, 27, 40, 46, 56, 60, 82, 88}.
What is a stem-and-leaf plot?In this plot, the first digit is 'stem' and the last digit is a 'leaf'.
And this plot is used to describe the quantitative data.
The stem-and-leaf plot shows the first digit (the stem) of each data point followed by the second digit (the leaf) of each data point. For example, the first row of the plot shows a stem of 1 and two leaves of 7, which corresponds to the number 17 in the data set. Similarly, the second row shows a stem of 2 and a leaf of 7, which corresponds to the number 27 in the data set.
Therefore, the correct option is:
{17, 27, 40, 46, 56, 60, 82, 88}.
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