The probability that the sample mean of 90 test takers falls within 10 points of the population mean of 502 is approximately 0.6578.
To find the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test, we need to calculate the probability using the standard normal distribution.
Given:
- Population mean [tex](\(\mu\))[/tex]: 502
- Sample size[tex](\(n\))[/tex]: 90
- Standard deviation [tex](\(\sigma\))[/tex] of the population (assumed known or provided): Let's assume it is 100 (for example purposes).
We are looking for the probability that the sample mean[tex](\(\bar{X}\))[/tex] falls within 10 points of the population mean (502 ± 10).
Step 1: Calculate the standard error of the mean (SEM):
[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} \][/tex]
[tex]\[ SEM = \frac{100}{\sqrt{90}} \][/tex]
[tex]\[ SEM = \frac{100}{9.4867} \][/tex]
[tex]\[ SEM \approx 10.548 \][/tex]
Step 2: Convert the deviation of ±10 points from the mean into a z-score using the standard normal distribution:
[tex]\[ z = \frac{\text{sample mean} - \mu}{SEM} \][/tex]
For the upper bound:
[tex]\[ z_{\text{upper}} = \frac{502 + 10 - 502}{10.548} \][/tex]
[tex]\[ z_{\text{upper}} = \frac{10}{10.548} \][/tex]
[tex]\[ z_{\text{upper}} \approx 0.9497 \][/tex]
For the lower bound:
[tex]\[ z_{\text{lower}} = \frac{502 - 10 - 502}{10.548} \][/tex]
[tex]\[ z_{\text{lower}} = \frac{-10}{10.548} \][/tex]
[tex]\[ z_{\text{lower}} \approx -0.9497 \][/tex]
Step 3: Find the cumulative probabilities using the standard normal distribution table or a calculator:
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) \][/tex]
Using a standard normal distribution table or a calculator, find:
[tex]\[ P(Z \leq 0.9497) \approx 0.8289 \][/tex]
[tex]\[ P(Z \leq -0.9497) \approx 0.1711 \][/tex]
Step 4: Calculate the probability that the sample mean falls within 10 points of the population mean:
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.8289 - 0.1711 \][/tex]
[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.6578 \][/tex]
Therefore, the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 is approximately [tex]{0.6578} \).[/tex]
Compare and contrast the absolute value of a real number to that of a complex number
Answer:
The absolute value of a real number is the distance from 0 on the number line. The absolute value of a complex number is the distance from the origin in the complex plane. Both are distances, and therefore both are positive values. You need to use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
Step-by-step explanation:
Use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
What is a complex number?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfies the equation i² = 1.
The absolute value of a real number is the distance from 0 on the number line. The absolute value of a complex number is the distance from the origin in the complex plane.
Both are distances, and therefore both are positive values. You need to use the distance formula or the Pythagorean theorem to calculate the absolute value of a complex number.
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which formula can be used to describe the sequence? 1.2, 3, 7.5, 18, 7.5, ...
Answer:
Option A) [tex]1.2(2.5)^{x-1}[/tex]
Step-by-step explanation:
We are given a series:
[tex]1.2, 3, 7.5, 18.75, ...[/tex]
We know that the given series is a geometric series as
[tex]\displaystyle\frac{3}{1.2} = \frac{7.5}{3} = \frac{18.75}{7.5} = 2.5[/tex]
Geometric Series:
A geometric series is a series with a constant ratio between successive terms. The first term is represented by aIn the given series a = 1.2The common ratio is denoted by rFor the given series r = 2.5The [tex]n^{th}[/tex] term of a geometric series is given by:
[tex]a_n = a(r)^{n-1}[/tex]
[tex]a_1= 1.2\\a_2 = 1.2(2.5)^{2-1} = 3\\a_3 = 1.2(2.5)^{3-1} = 7.5\\a_4 = 1.2(2.5)^{4-1} = 18.75[/tex]
Thus, the general term of the given series can be formulated with the help of [tex]f(x) = 1.2(2.5)^{x-1}[/tex]
Option A) [tex]1.2(2.5)^{x-1}[/tex]
A bacteria has a doubling period of 10 days. If there are 2100 bacteria present now, how many will there be in 45 days?
First we must find the daily growth rate (Don't round up, keep all the decimal places) .
The growth rate is:
There will be (_) bacteria.
Describe how to substitute an ordered pair into an equation
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I will give you brainlyest awnser
f(x) = 2x^2 + 3 and g(x) = x^2 - 7, find (f-g)(x)
A) 3x^2 - 10
B) x^2 - 4
C) x^2 + 10
D) 3x^2 - 4
Let's solve for a.y=2x2+3andgxStep 1: Flip the equation.3adgnx+2x2=yStep 2: Add -2x^2 to both sides.3adgnx+2x2+−2x2=y+−2x23adgnx=−2x2+yStep 3: Divide both sides by 3dgnx.3adgnx3dgnx=−2x2+y3dgnxa=−2x2+y3dgnx answer :a=−2x2+y3dgnx
One side of a rectangle is 18 inches and the other side is x inches. What values of x will make the perimeter more than 56 inches?
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
(0, 6) and (2, 0)
(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)
if 45 people enrolled in a psychology course but only 35 completed it, what percent of the students completed the course
Which value of r indicates a stronger correlation: r equals=0.828 or r equals= −0.879? explain your reasoning?
A value of r = 0.828 indicates a stronger positive correlation, while r = -0.879 indicates a stronger negative correlation.
Explanation:A stronger correlation is indicated by a value closer to 1 or -1. In this case, r = 0.828 indicates a stronger positive correlation, whereas r = -0.879 indicates a stronger negative correlation. The closer the absolute value of r is to 1, the stronger the correlation. A value of r = 0.828 suggests a strong positive relationship between two variables, while a value of r = -0.879 suggests a strong negative relationship.
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Type the integer that makes the following addition sentence true:
+ 4 = 4
Monica wants to make sure that her sentences are easily understood. how long should she make them?
a. an average of 28 words
b. no more than 8 words
c. at least 30 words
d. an average of 20 words
The volume of a cone is 31.4 cm3 and the radius is 2 cm. What is the height of the cone? Use 3.14 for π. Round to the nearest tenth, if needed.
A) 22.5 cm
B) 7.5 cm
C) 15 cm
D) 41.9 cm
there is 4/5 lb of sand in the class science supplies. if one scoop of sand weighs 1/20 lb, how many scoops of sand can maria get from the class supplies and still leave 1/2 lb in the supplies
A culture of 2.4×10^11 bacteria is in petri dish A. A culture of 8×10^9 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
The number of bacteria in petri dish A is 30 times greater than the number in petri dish B. This is calculated by dividing 2.4 × 10^11 by 8 × 10^9.
To determine how many times greater the number of bacteria in petri dish A is compared to petri dish B, we need to divide the number of bacteria in petri dish A by the number in petri dish B.
Given:
Petri dish A: 2.4 × 10^11 bacteriaPetri dish B: 8 × 10^9 bacteriaThe calculation is:
2.4 × 10^11 / 8 × 10^9 = 3 × 10^1 = 30
Therefore, the number of bacteria in petri dish A is 30 times greater than in petri dish B.
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what inequality represents the verbal expression? 8 less than a number n is less than 11
The inequality representing the verbal expression '8 less than a number n is less than 11' is written as 'n < 19'. This is found by adding 8 to both sides of the inequality 'n - 8 < 11'.
Explanation:The inequality that represents the verbal expression '8 less than a number n is less than 11' can be translated into a mathematical inequality as follows. First, '8 less than a number n' means you take 8 away from n, which is written as n - 8. Then, this quantity being 'less than 11' is represented by the inequality n - 8 < 11. To find the range of values for n, we solve this inequality.
Step 1: Add 8 to both sides of the inequality to isolate n -
n - 8 + 8 < 11 + 8
Step 2: Simplify -
n < 19
Therefore, the inequality symbol that represents the verbal expression is n < 19.
The inequality that represents the verbal expression '8 less than a number n is less than 11' is 8 < n < 11. The symbol '<' represents 'less than' and since the number n is between 8 and 11, we use the inequality symbol '<' twice.
The inequality that represents the verbal expression '8 less than a number n is less than 11' is 11 > n - 8 > 8.
Explanation:The inequality that represents the verbal expression '8 less than a number n is less than 11' is 11 > n - 8 > 8. This inequality states that the number n, decreased by 8, is greater than 8 and less than 11.
One half of a number y is more than 22
Answer:
Inequality: [tex]\frac{y}{2}>22[/tex]
Solution: [tex]y>44[/tex]
Step-by-step explanation:
We are supposed to write and solve an inequality for the given verbal description.
One half of a number y would be y divided by 2: [tex]\frac{y}{2}[/tex].
Since one half of a number y is more than 22, so we can set an inequality as:
[tex]\frac{y}{2}>22[/tex]
Multiply both sides by 2:
[tex]\frac{y}{2}*2>22*2[/tex]
[tex]y>44[/tex]
Therefore, the solution to our given inequality is any value of y greater than 44.
Jacqueline leaves city a at 2:00 p.m. and drives at a constant speed, traveling west on i-90. she passes city b, 40 mi from city a, at 2:50 p.m. (a) find a linear function d that models the distance (in mi) she has traveled after t min.
Jacqueline's speed is 0.8 miles per minute. The linear function representing the distance she has traveled in t minutes is d(t) = 0.8t. This equation means Jacqueline would have covered 0.8t miles after any given time t.
Explanation:The subject of this question is a linear function in mathematics, more specifically, it is about the concept of speed and distance. The question describes the journey of a person named Jacqueline who is traveling at a constant speed.
Given that city B is 40 miles from city A and it took Jacqueline 50 minutes to cover that distance, we can easily calculate her speed. Speed = Distance / Time. Therefore, her speed is 40 miles / 50 minutes = 0.8 miles per minute.
The linear function d, which models the distance she has traveled after t minutes would, therefore, be d(t) = 0.8t. The coefficient 0.8 indicates the speed, and the variable t is the time spent traveling. So, after any given number of minutes t, Jacqueline would have covered 0.8t miles on her journey.
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Which expression shows the result of applying the distributive property to 3(2x−6) ?
A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3
How many 7/8 yard long scarves can I make from 156 feet of fabric
0.09 is 10 times as much as
Jackson's mom gave him $1.50 each day to buy his lunch. How much money would she give him each week?
A)
$1.50 x 5 = $15.00
B)
$1.50 x 5 = $0.75
C)
$1.50 x 5 = $75.00
D)
$1.50 x 5 = $7.50
Option D. $1.50 x 5 = $7.50
For week:
$1.50 x 5
= $7.50
So, the correct answer is D) $1.50 x 5 = $7.50.
121 bricks in 16.5 minutes 22 brings in m minutes
Which statement is true about this argument? Premises: If a triangle has an angle that measures 150°, then it is an obtuse triangle. △JKL is an obtuse triangle. Conclusion: △JKL has an angle that measures 150°.
A) The argument is not valid because the premises are not true.
B) The argument is valid by the law of syllogism.
C) The argument is not valid because the conclusion does not follow from the premises.
D) The argument is valid by the law of detachment.
Find the slope of the graph of the function y=5x/x-2 at (3,15). Then find an equation for the line tangent to the graph at that point.
The slope of the graph at the point (3,15) is -10. The equation of the tangent line at that point is y = -10x + 45.
Explanation:To find the slope of the graph, we need to differentiate the equation y=5x/(x-2). Using the quotient rule, the derivative of this equation is (5(x-2) - 5x)/(x-2)². Simplifying this further, we get -10/(x-2)². Now, substitute the x-coordinate of the point (3,15) into the derivative to find the slope at that point. Substituting x=3, we get a slope of -10/1 = -10.
To find the equation of the tangent line at the point (3,15), we use the point-slope form of a line, y - y1 = m(x - x1). Substituting the slope (-10) and the coordinates of the point (3,15) into this equation, we get y - 15 = -10(x - 3). Simplifying further, we get y - 15 = -10x + 30. Rearranging the equation, we get y = -10x + 45. Therefore, the equation of the tangent line to the graph at the point (3,15) is y = -10x + 45.
An investor bought 400 shares of stock, some at $7.00 per share and some at $1.00 per share. If the total cost was $1450.00, how many shares of each stock did the investor buy?
The investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
Explanation:To solve this problem, you can set up a system of equations. Let x be the number of shares bought at $7.00 per share and y be the number of shares bought at $1.00 per share.
From the information given, we know that:
x + y = 400 (equation 1)7x + y = 1450 (equation 2)To solve the system of equations, you can use the substitution method or the elimination method.
Using the elimination method, multiply equation 1 by 7 to make the coefficients of x in both equations equal:
7(x + y) = 7(400)7x + 7y = 2800 (equation 3)Now, subtract equation 2 from equation 3 to eliminate x:
(7x + 7y) - (7x + y) = 2800 - 14506y = 1350y = 225Substitute the value of y into equation 1 to find x:
x + 225 = 400x = 175Therefore, the investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
What is 20% of 1630?
if I fail this I'm gonna fail the quarter. please help
Quadrilateral PQRS is shown below. Which of the following transformations of ΔPTS could be used to show that ΔPTS ≅ ΔQTR ?
A reflection over line segment QS
2) A reflection over line segment PR
3) A reflection over line m
4) A reflection over line l
The transformation that would show triangle PTS is congruent to triangle QTR in quadrilateral PQRS is a reflection over the line segment PR, assuming PQRS is a parallelogram.
Explanation:The question involves identifying which transformation of triangle PTS would show that it is congruent to triangle QTR in quadrilateral PQRS. Without a diagram, it's difficult to provide a specific answer. However, the properties given refer to the symmetric treatment of the sides of a parallelogram and parallel lines. Based on the axioms provided, if PQRS is a parallelogram, then any reflection over the line connecting opposite corners (diagonals) would make two triangles inside the parallelogram congruent. This is because reflections over a line preserve the size and shape of a geometric figure while flipping it over the line. Since PTS and QTR share point T, reflect triangle PTS over the line containing this shared point, which is the line TR or line segment PR, assuming PQRS is a parallelogram.
There are eight rooms in Fern's home . Two of them are used for her office space. What percentage of the home's rooms is not used for the office space?
Please help me will pick brainliest answer with more info!!!
How to write one hundred seventy five and one hundred fifty five thousandth in standard form