Answer:
Probability that at least 1 of those sampled have access to on-line services at home is 0.9648.
Step-by-step explanation:
We are given that current estimates suggest that 20% of people with home-based computers have access to on-line services.
Suppose that 15 people with home-based computers were randomly and independently sampled.
The above situation can be represented through binomial distribution;
[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 15 people
r = number of success = at least one
p = probability of success which in our question is % of people
who have access to on-line services at home, i.e.; p = 20%
Let X = Number of people who have access to on-line services at home
So, X ~ Binom(n = 15, p = 0.20)
Now, probability that at least 1 of those sampled have access to on-line services at home is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1- \binom{15}{0}\times 0.20^{0} \times (1-0.20)^{15-0}[/tex]
= [tex]1- (1\times 1 \times 0.80^{15})[/tex]
= 1 - 0.0352 = 0.9648
Hence, the required probability is 0.9648.
The following problem can be solved using the binomial distribution.
Binomial distributionA common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
There is 96.481% chance that at least 1 of those sampled have access to online services at home.
Given to usThe online access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to online services.Suppose that 15 people with home-based computers were randomly and independently sampled. SolutionFor the values,As given, 20% of people with home-based computers have access to online services. therefore, the probability of a person having access to online services is also 20%. thus, p = 20% = 0.2We know that for any event the sum of all probability is 1. therefore, the probability of a person not having access to online services is (1-p). thus, q = (1-0.20) = 0.80It is already stated in the sentence that the sample is been done on 15 people. therefore, the sample size is n = 15.We need the probability that at least 1 of those sampled have access to online services at home, therefore, x ≥ 1.ProbabilitySubstituting the values in a binomial distribution,
[tex]P(x\geq 1) = 1- P(0)[/tex]
[tex]P(x\geq 1) = 1-\ ^{15}C_0\times [0.20^0]\times [0.80^{(15-10)}]\\\\ P(x\geq 1)=1-\ 0.032\\\\ P(x\geq 1) = 0.96481\\\\ [/tex]
Hence, there is 96.481% chance that at least 1 of those sampled have access to online services at home.
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When measuring miles using a telescope, surveyors made an error of 6.5 feet per mile. If the total error was 55.25 feet, how
many miles were measured?
A 8.5
B
48.75
C
61.75
D
359.125
A. 8.5.
55.25 feet / 6.5 feet = 8.5 miles.
what is a telescope?A telescope is an optical tool using lenses, curved mirrors, or a combination of both to look at distant objects, or various devices used to look at distant objects by means of their emission, absorption, or reflection of electromagnetic radiation.
There are three main types of telescope. These are
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The Central Company manufactures a certain specialty item once a month in a batch production run. The number of items produced in each run varies from month to month as demand fluctuates. The company is interested in the relationship between the size of the production run (x) and the number of hours of labor (y) required for the run. The company has collected the following data for the ten most recent runs. Number of items: 40 30 70 90 50 60 70 40 80 70 Labor (hours): 81 60 137 180 99 117 140 74 159 143 (a) Find a point estimate for the number of hours of labor required, on average, when 60 units are produced. (Round your ans
Answer:
p value = 0.0000 < 0.05
We reject H0
Hence the claim is significant
Step-by-step explanation:
See attached image
Giving brainliest for CORRECT awnser.
Answer:
12
Step-by-step explanation:
x^2 -bx +36
A perfect square trinomial is of the form
a^2 -2abx +b^2
x^2 -bx +6^2
a =1 and b = 6
2ab = 2*1*6 = 12
determine the percent change from 171.33 to 201.59
Answer:15
Step-by-step explanation:
%change=(201.59-171.33)/201.59 x 100
%change=30.26/201.59 x 100
%change=0.15 x 100
%change=15
If a basketball player makes 2 baskets for every 5 shots and he keeps getting baskets at the same rate, how many baskets will he get if he takes 100 shots?
Answer:
i thinl it would be 200 or 1000
the attendance at a conference was 23,000, rounded to the nearest hundred. what is the difference between the largest and smallest possible attendances
Answer:
largest= 23,049
smallest= 22,950
4. Determine which of the following relations on the given sets are reflexive, symmetric, antisymmetric and/or transitive: a) ℛ = {(1,5), (5,1), (1,1), (2,2), (3,3)(4,4)} oooo ???????? = {1,2,3,4,5} Write the matrix representation of this relation. b) ???????? = {(1,4), (1,2), (2,3), (3,4), (5,2), (4,2), 1,3)} oooo ???????? = {1,2,3,4,5} Write the matrix representation of this relation.
Answer:
(a)
Reflexivity
Is not reflexive
Symmetry
Is symmetric
Anti-Symmetry
is not antisymmetric.
Transitivity
It is transitive
[tex]R = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 & 0 \\0 & 0& 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 0& 0& 0 & 1 \end{pmatrix}[/tex]
(b)
Reflexivity
Is not reflexive
Symmetry
Is not symmetric
Anti-Symmetry
It is antisymmetric
Transitivity
So is NOT transitive.
[tex]R = \begin{pmatrix} 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 1& 0 & 0& 0 \\0 & 1& 0& 0 & 0 \end{pmatrix}[/tex]
Step-by-step explanation:
(a)
Reflexivity
Is not reflexive because 5 is not related to 5.
Symmetry
Is symmetric because 1R5 .and 5R1
Anti-Symmetry
If it is symmetric then it is not antisymmetric.
Transitivity
It is transitive because 1R5 5R1 and 1R1.
[tex]R = \begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 & 0 \\0 & 0& 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 0& 0& 0 & 1 \end{pmatrix}[/tex]
(b)
Reflexivity
Is not reflexive no element of the set is related to itself.
Symmetry
Is not symmetric because (1,4) belongs to the relation but (4,1) does not belong to the relation . And similarly you can do the same with all pairs and none of them will satisfy the condition.
Anti-Symmetry
It is symmetric because for every element if aRb then "b" is NOT related to "a"
Transitivity
A relation can't be antisymmetric and transitive. So is NOT transitive.
[tex]R = \begin{pmatrix} 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 0 \\0 & 0& 0 & 1 & 0 \\0 & 1& 0 & 0& 0 \\0 & 1& 0& 0 & 0 \end{pmatrix}[/tex]
On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5). The graph shows the function f(x) = |x – h| + k. What is the value of k? k = –2.5 k = –1 k = 1 k = 2.5
9514 1404 393
Answer:
(a) k = –2.5
Step-by-step explanation:
When the function f(x) is transformed to f(x -h) +k, the graph is translated h units right and k units up.
If the absolute value function has its original vertex of (0, 0) moved to (1, -2.5), then (h, k) = (1, -2.5).
The value of k is -2.5.
_____
Additional comment
The above answer applies to the given problem statement. The question asked in the comment has a vertex of (0, 2.5), so (h, k) = (0, 2.5) for that question.
If you're going to copy the answer, make sure it is the answer to the question you're looking at.
In an absolute value function expressed as f(x) = |x – h| + k, the value of k corresponds to the y-coordinate of the function's vertex. In this case, as the vertex is at the point (1, -2.5), the value of k is -2.5.
The student's question relates to the concepts of Two-Dimensional (x-y). Graphing and the graphing of the absolute value function. It is vital to remember that the vertex of an absolute value graph in the form f(x) = |x – h| + k corresponds to the point (h, k) on the Cartesian coordinate plane. The student states that the vertex is at the point (1, -2.5), so based on our function analysis, the value of k, which represents the y-coordinate of the vertex, is -2.5. Therefore, the correct answer is k = -2.5.
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Consider the following probability distribution for stocks A and B: State Probability Return on Stock A Return on Stock B 1 0.10 10 % 8 % 2 0.20 13 % 7 % 3 0.20 12 % 6 % 4 0.30 14 % 9 % 5 0.20 15 % 8 % The standard deviations of stocks A and B are ________ and ________, respectively. Group of answer choices 2.5%; 1.1% 1.5%; 1.1% 1.5%; 1.9% 3.2%; 2.0%
Answer:
None of the above. The correct answer is 1.47%, 1.10%.
Step-by-step explanation:
The first thing to do is to calculate the Expected return of Stock A and Stock B.
For A;
Probability. Return.
0.1.= 0.1 × 10% = 1.00%
0.2= 0.2 × 13% = 2.60%
0.2= 0.2× 12% = 2.40%.
0.3= 0.3 × 14% = 4.20%
0.2= 0.2 × 15% = 3.00%
Total = 13.20%.
For B;
Probability. Return.
0.1= 0.1 × 8% = 0.80%
0.2= 0.2 × 7% = 1.40%
0.2.= 0.2 × 6% = 1.20%
0.3.= 0.3 × 9% =2.70%
0.2.= 0.2 × 8%= 1.60%
Total = 7.70%.
Hence, the Expected return of Stock A and B = 13.20% and 7.70%. respectively.
Now, let us find the Standard deviation of Stock A and the Standard deviation of Stock B.
For A
For individual value of A, we use the following formula;
(A - Expected return of Stock A)^2 × probability.
For instance,
(10% - 13.20%)^2 × 0.1 =0.000102.
(13% - 13.20%)^2 × 0.2= 0.000001.
(12% - 13.20%)^2 × 0.2 = 0.000029.
(14% - 13.20%)^2 × 0.3 =0.000019.
(15% - 13.20%)^2 × 0.2 = 0.000065.
Which gives us the following values;
0.000102, 0.000001, 0.000029, 0.000019, 0.000065.
The next thing to do is to find the variance (that is the addition of all the values above) and the value for the square root of variance which is the standard deviation.
√( 0.000102 + 0.000001 + 0.000029 + 0.000019 + 0.000065) = 0.000216.
Thus, variance = 0.000216, square root of variance= 0.014697(1.47%).
For B;
We follow as the one above.
(B - Expected return of Stock A)^2 × probability.
We have values as;
0.000001, 0.000010, 0.000058, 0.000051, 0.000002.
√ ( 0.000001 + 0.000010 + 0.000058 +0.000051 + 0.000002).
= 0.011( 1.10%).
To find the standard deviations of stocks A and B, calculate the expected returns and then use the variance formula to determine the standard deviations by taking the square root of the variance for each stock.
Explanation:The standard deviations of stocks A and B can be calculated using the probabilities and the returns given in the probability distribution. First, we calculate the expected return for each stock by multiplying the return by the probability of each state and summing it up. Then we use the formula for standard deviation, which is the square root of the expected value of the squared deviations from the mean.
For Stock A, we calculate the expected return (μA) and the variance (σA2) before finding the standard deviation (σA). The same steps are taken for Stock B to find its expected return (μB) and standard deviation (σB). Without the detailed calculations, we are unable to provide the exact values for the standard deviations, but by following these methods, you can determine which of the given options is correct for both stocks.
What is the following product? Assume b greater-than-or-equal-to 0
StartRoot b EndRoot times StartRoot b EndRoot
b StartRoot b EndRoot
2 StartRoot b EndRoot
b
b2
Answer:
c).b
Step-by-step explanation:
e2020
The result of the product [tex]\sqrt b \times \sqrt b =b[/tex] is b
The product is represented as:-
[tex]\sqrt b \times \sqrt b[/tex]
Multiply the roots
[tex]\sqrt b \times \sqrt b =\sqrt{b^2}[/tex]
Rewrite the above expression as:
[tex]\sqrt b \times \sqrt b =b^{\frac 12 \times 2}[/tex]
Multiply 1/2 and 2
[tex]\sqrt b \times \sqrt b =b^{ 1}[/tex]
Express b^1 as b
[tex]\sqrt b \times \sqrt b =b[/tex]
Hence, the result of product [tex]\sqrt b \times \sqrt b =b[/tex] is b
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A study was completed in Florida. In southern Florida, the study involved 3,000 patients; 54% of them experienced flulike symptoms during the same month. The study had a margin of error of 1.8%. What does that mean for the study? The confidence interval is between 52.2% and 55.8%. The confidence interval is between 50.4% and 57.6%. The confidence interval is between 53% and 55%. The confidence interval is between 30% and 97.2%.
Answer:
A (52,2%, 55,8%)
Step-by-step explanation:
To get the confidence interval, we have to add the margin of error to the point estimator.
The middle of the interval is 54%, and the ME is 1.8%. Don't forget that this means ±1.8%!
54 - 1.8 = 52.2%
54 + 1.8 = 55.8%
So our confidence interval is (52,2%, 55,8%) and the answer is A.
The margin of error of 1.8% in the study indicates that the true percentage of patients with flu-like symptoms is likely between 52.2% and 55.8%.
The margin of error in the study from Florida is 1.8%.
This means that we can be confident that the true percentage of patients experiencing flu-like symptoms is within 1.8% of the observed 54%, above and below this value.
To calculate the confidence interval, we add and subtract the margin of error from the observed percentage. Therefore, the confidence interval would be from 54% - 1.8% to 54% + 1.8%, which is between 52.2% and 55.8%.
Best gets Brainliest! Please help im desperate
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms:
2 – 11 x 2 – 8 x + 6 x 2
The Bureau of the Census reports the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida. To see if their commuting times appear to be any different in the winter, random samples of 40 drivers were surveyed in each city and the average commuting time for the month of January was calculated for both cities. The results are provided below. Miami (X1) Baltimore (X2) Sample size 40 40 Sample mean 28.5 min 35.2 min Population standard deviation 7.2 min 9.1 min At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? What is the test statistic? Round to 3 decimal places.
Answer:
[tex]z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652[/tex]
Now we can calculate the p value since we are conducting a bilateral test the p value would be:
[tex]p_v =2*P(z<-3.652)=0.00026[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.
Step-by-step explanation:
Information provided
[tex]\bar X_{1}=28.5[/tex] represent the mean for Miami
[tex]\bar X_{2}=35.2[/tex] represent the mean for Baltimore
[tex]\sigma_{1}=7.2[/tex] represent the population standard deviation for Miami
[tex]\sigma_{2}=9.1[/tex] represent the population standard deviation for Baltimore
[tex]n_{1}=40[/tex] sample size selected for Miami
[tex]n_{2}=10[/tex] sample size selected for Baltimore
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test
Hypothesis to analyze
We want to check if the commiting times are different in the winter for the two cities, so then the system of hypothesis are:
Null hypothesis:[tex]\mu_{1} = \mu_{2}[/tex]
Alternative hypothesis:[tex]\mu_{1} \neq \mu_{2}[/tex]
Since we know the population deviations the statistic for this case is given by:
[tex]z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
Replacing the info provided we got:
[tex]z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652[/tex]
Now we can calculate the p value since we are conducting a bilateral test the p value would be:
[tex]p_v =2*P(z<-3.652)=0.00026[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.
Use the triangle shown to find the ratios.
cos(A) =
tan(C) =
Triangle A B C is shown. Angle A B C is a right angle. The length of A B is 10 feet, the length of C B is 24 feet, and the length of hypotenuse A C is 26 feet.
Answer:
cos (A) =5/13
tan (C) =5/12
Step-by-step explanation:
The triangle for the problem is produced and attached.
cos (A)=Adjacent/Hypotenuse
cos (A) = 10/26 =5/13
Similarly,
tan (C)=Opposite/Adjacent
tan (C)=10/24 =5/12
Answer:
Cos(A) = 5/13 or 10/26
Tan(C) = 5/12 or 10/24
Step-by-step explanation:
I did it on edge :)
what is the volume of the rectangular prism
Answer:
Step-by-step explanation:
V=WHL
Answer:
I think V= 256
Step-by-step explanation:
1 point) The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 65 with a standard deviation of 5.3. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg
Answer:
The probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
Step-by-step explanation:
The random variable X can be defined as the amount of oxygen an athlete takes in.
The mean maximum oxygen uptake for elite athletes is, μ = 65 ml/kg.
The standard deviation is, σ = 5.3 ml/kg.
The random variable X is approximately normally distributed.
Now to compute probabilities of a normally distributed random variable, we first need to convert the value of X to a z-score.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The distribution of these z-scores is known as a Standard normal distribution, i.e. [tex]Z\sim N(0, 1)[/tex].
A normal distribution is a continuous distribution. So, the probability at a point on a normal curve is 0. To compute the exact probabilities we need to apply continuity correction.
Compute the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg as follows:
P (X ≥ 50) = P (X > 50 + 0.50)
= P (X > 50.50)
[tex]=P(\frac{x-\mu}{\sigma}>\frac{50.50-65}{5.3})[/tex]
[tex]=P(Z>-2.74)\\=P(Z<2.74)\\=0.99693\\\approx 0.9970[/tex]
Thus, the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is 0.9970.
write the equation of the circle graphed below
Answer:
The equation of the circle is
(x + 2)² + (y + 2)² = 9
Centered at (-2, -2), with radius of 3 units.
Step-by-step explanation:
The general equation of a circle is given as
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
Looking at the graph, the center is the red dot. It corresponds to -2 on the y-axis, and -2 on the x-axis. So, the center (h, k) is (-2, -2).
The radius is the distance from the center of the circle to the edge of the circle. The red dot is the edge of the circle, there are 3 lines that represent 3 units, so we have a radius of 3 units.
Using these in the general equation, we have
[x - (-2)]² + [y - (-2)]² = 3²
(x + 2)² + (y + 2)² = 9
And this is the equation.
Answer:
(x+2)^2 + (y+2)^2= 0.5625
Step-by-step explanation:
10. The scores on the verbal section of the Graduate Records Examination (GRE)
are approximately normally distributed with a mean of 150 and a standard
deviation of 8.5. What is the probability that a randomly selected score on the
verbal section is higher than 1657
Answer:
The probability that a randomly selected score on the verbal section is higher than 165 is 0.0392
Step-by-step explanation:
We are given that The scores on the verbal section of the Graduate Records Examination (GRE) are approximately normally distributed with a mean of 150 and a standard deviation of 8.5.
Mean = [tex]\mu = 150[/tex]
Standard deviation =[tex]\sigma = 8.5[/tex]
We are supposed to find the probability that a randomly selected score on the verbal section is higher than 165 i.e.P(x>165)
Formula :[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{165-150}{8.5}[/tex]
Z=1.76
Refer the z table for p value
P(x<165)=0.9608
P(x>165)=1-P(x<165)=1-0.9608=0.0392
Hence the probability that a randomly selected score on the verbal section is higher than 165 is 0.0392
If a car can go 300 miles on 12 gallons, how far can it go on 1 gallon
Answer:
The car can go 25 miles on 1 gallon.
Step-by-step explanation:
300 divided by 12 equals 25. Therefore, the car can go 25 miles on 1 gallon.
Answer:
25 miles
Step-by-step explanation:
Let distance = x
Gallons Miles
12. 300
1. x
12x = 300
x = 300/12
x = 25 miles
A car can go 25 miles on 1 gallon.
x=23y+4 solve for x and graph
Answer:
X=4
for the graph, the point would be (4,0)
Miranda says that the triangle below represents the cross section of the rectangular pyramid shown.What mistake might miranda have made
Answer:
Miranda may have made the mistake of mismatching
Step-by-step explanation:
See attached a rough sketch of Cross sections of rectangular and triangular pyramids
Miranda made the mistake of not properly identifying the cross section of a rectangular pyramid which has a cross section of a rectangle.
A triangular pyramid has a triangular cross section
The file CEOSAL2.RAW contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary. (i) Estimate a model relating annual salary to firm sales and market value. Make the model of the constant elasticity variety for both independent variables. Write the results out in equation form. (ii) Add profits to the model from part (i). Why can this variable not be included in logarithmic form
Find the given attachment for the solution
A model relating a CEO's annual salary to firm's sales, market value, and profits is proposed. The equation takes a logarithmic form of sales and market value for the elasticity. Profits cannot take a logarithmic form due to the possibility of negative values.
Explanation:The objective of this question is to build a model relating CEO's annual salary to firm sales, market value, and profits, using the data from CEOSAL2.RAW. The model would be a constant elasticity variety for the sales and market variables. The standard form of a constant elasticity model is ln(Y) = a + b1*ln(X1) + b2*ln(X2) + u, where Y represents the dependent variable (CEO's annual salary), X1 and X2 represent independent variables (firm sales and market value).
Now adding profits to the model, your equation would be: ln(Y) = a + b1*ln(X1) + b2*ln(X2) + b3*X3 + u, where X3 denotes the firm's profits. It is not in logarithmic form because profits can be negative, and the natural log of a negative number is undefined in real numbers.
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In a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.
Answer:
95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].
Step-by-step explanation:
We are given that in a random sample of 41 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 51 months, with a standard deviation of 11 months.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean length of sentencing = 51 months
[tex]s[/tex] = sample standard deviation = 11 months
n = sample of criminals = 41
[tex]\mu[/tex] = population mean length of sentencing
Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.021 < [tex]t_4_0[/tex] < 2.021) = 0.95 {As the critical value of t at 40 degree of
freedom are -2.021 & 2.021 with P = 2.5%}
P(-2.021 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.021) = 0.95
P( [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.021 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.021 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]51-2.021 \times {\frac{11}{\sqrt{41} } }[/tex] , [tex]51+2.021 \times {\frac{11}{\sqrt{41} } }[/tex] ]
= [47.53 , 54.47]
Therefore, 95% confidence interval for the mean length of sentencing for this crime is [47.53 months , 54.47 months].
What is the area of the rectangle, in square centimeters? A rectangle with length 12 centimeters and width 5 centimeters. 17 34 30 60
A manufacturer of cream filled donuts wants to make sure that it's automatic filling process is on target. Based On sample of 25 donuts the mean weight of cream filling is estimated to be 15 grams with a standard deviation of 1.5 grams. however, the quality control inspectors wish to estimate the mean wright of cream filling mor accurately so that they can be 99% confident that it is within 0.25 grams of the true mean. How many donuts should they sample?
To estimate the true mean weight of the cream filling within 0.25 grams with 99% confidence, the quality control inspectors should sample approximately 384 donuts. This is calculated using statistical techniques for sample size determination.
Explanation:In order to find out how many donuts the quality control inspectors should sample, we need to utilize the formula for sample size in statistics, which is n = (Z^2 * σ^2 * N) / E^2 . In this case, 'Z' is the Z-score which corresponds to the desired confidence level, σ is the standard deviation of the sample data, E is the desired margin of error, and N is the population size.
For a 99% confidence level, the Z-score is 2.58. Given the standard deviation(σ) is 1.5 grams, and the desired margin of error(E) is 0.25 grams, we can substitute these values into the equation to calculate the sample size(n).
Substituting these values: n = (2.58^2 * 1.5^2) / 0.25^2. n becomes approximately 384.
Therefore, the quality control inspectors should sample approximately 384 donuts to be 99% confident that their estimate of the true mean weight of cream filling is within 0.25 grams of the true mean.
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Luther takes 45 bottles of water on a camping trip. If he drinks 80% of them how many does he have left
Answer:
9 bottles
Step-by-step explanation:
If Luther drinks 80% of the water bottles, then he has 100% - 80% = 20% of his bottles left. Therefore, we find that he has 45 * 0.20 = 9 bottles left.
Answer:
9
Step-by-step explanation:
45-(45x0.80)=9
A right rectangular prism with square bases has a height of 20cm and a volume of 800 cubic centimeters. Which statements describe the prism?
Answer:
The area of the rectangular prism is 40cm²
Step-by-step explanation:
To calculate the volume of a rectangular prism we have to use the following formula:
a = area
v = volume = 800 cm³
h = height = 20 cm
v = a * h
we replace the values that we know
800cm³ = a * 20cm
800cm³ / 20cm = a
40cm² = a
v = 70ft³
The area of the rectangular prism is 40cm²
Pls help me I reallyyyyy don't understand
Answer:
9
Step-by-step explanation:
range is the range from the lowest # through the biggest # in other words subtract the smaller number from the bigger number
a classmate says the first step to solve the equation 12(3g-9)=99 is to add to both sides do you agree
Answer:
NoStep-by-step explanation:
[tex]12(3g - 9) = 99 \\ 36g - 108 = 99 \\ 36g = 99 + 108 \\ 36g = 207 \\ \frac{36g}{36} = \frac{207}{36} \\ g = 5.75[/tex]
En un mapa, 1 cm medido en el papel representa a 100 km
a. que distancia en la realidad habrá entre dos puntos que en el papel distan 3,3 cm?
b. que distancia en el papel habrá si en la realidad hay 1 800 km
porfa respondan