Mathematics, 14.04.2020 23:17 1031kylepoe03

The average price of a gallon of gasoline in Missouri was $2.77 (as of 10-25-10 according to the AAA Daily Fuel Gauge Report). Suppose it is known that σ^2=0.32. What is the probability that a sample of 72 gas stations taken that same week will have a sample mean within $0.15 of the population mean? (Hint: You may need to use as many as 4+ decimal places in your computations to come up with the correct answer!)

A. 0.9756
B. 0.0240
C. 0.0398
D. 0.4176
E. Almost 1 2128

Answers: 2

Show answers

Answers

Answer from: klivingston1012

A. 0.9756

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 2.77, \sigma = \sqrt{0.32} = 0.5657, n = 72, s = \frac{0.5657}{\sqrt{72}} = 0.0667$

What is the probability that a sample of 72 gas stations taken that same week will have a sample mean within $0.15 of the population mean?

This is the pvalue of Z when X = 2.77 + 0.15 = 2.92 subtracted by the pvalue of Z when X = 2.77 - 0.15 = 2.62. So

X = 2.92

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{2.92 - 2.77}{0.0667}$

Z = 2.25

Z = 2.25 has a pvalue of 0.9878

X = 2.62

$Z = \frac{X - \mu}{s}$

$Z = \frac{2.62 - 2.77}{0.0667}$

Z = -2.25

Z = -2.25 has a pvalue of 0.0122

0.9878 - 0.0122 = 0.9756

Answer from: Quest

2? if not the correct answer you might need to provide more information

step-by-step explanation:

Answer from: Quest

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has vertices $p(1,2),q(2,1),r(3,2),s(3,3)$ recall that for counterclockwise rotation about the origin, $(x,y)\rightarrow (-x,-y)$ when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will become $p1( - 1, - 2),q1( - 2, - 1),r1( - 3, - 2),s1( - 3, - 3)$ next, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain, $p'(1, - 2),q'(2, - 1),r'(3, - 2),s'(3, - 3)$ therefore the correct answer is c

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Will give find an equivalent function to f(x)=5(2)^3x. the 5(2)^3x means 5(2) to the 3x power answer choices: a: f(x)=125^x(8)^x b: f(x)=10^2x c: f(x)=40^x d: f(x)=5(8)^x

Answers: 3

Answer

Mathematics, 21.06.2019 15:30

Which answer is the solution set to the inequality |x|< 9? a. x< -9 or x> 9 b. x> -9 and x< 9 c. x> -9 or x< 9 d. x< 9 and x< 9

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Two cyclists 84 miles apart start riding toward each other at the samen time. one cycles 2 times as fast as the other. if they meet 4 hours later what is the speed (in miles) of the faster cyclists

Answers: 2

Answer

Mathematics, 21.06.2019 19:50

Which of the following describes the graph of y--4x-36 compared to the parent square root function? stretched by a factor of 2, reflected over the x-axis, and translated 9 units right stretched by a factor of 2, reflected over the x-axis, and translated 9 units left stretched by a factor of 2, reflected over the y-axis, and translated 9 units right stretched by a factor of 2, reflected over the y-axis, and translated 9 units left save and exit next submit

Answers: 1

Answer

You know the right answer?

The average price of a gallon of gasoline in Missouri was $2.77 (as of 10-25-10 according to the AAA...

Questions

Mathematics, 19.02.2020 23:36

What is the solution to the linear equation? 2/3x - 1/2 = 1/3 + 5/6x...