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The average price of a college math textbook is $162 and the standard deviation is $27. Suppose that 10 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of x? ~ N( b. For the group of 10, find the probability that the average price is between $161 and $167. c. Find the 95th percentile for the average textbook price for this sample size. $ (round to the nearest cent)

The average price of a college math textbook is $162 and the standard deviation is $27. Suppose that 10 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of x? ~ N( b. For the group of 10, find the probability that the average price is between $161 and $167. c. Find the 95th percentile for the average textbook price for this sample size. $ (round to the nearest cent)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Problem Statement:** The average price of a college math textbook is $162 and the standard deviation is $27. Suppose that 10 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. **Questions:** a. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\_\_, \_\_\_\_\_\_)\) b. For the group of 10, find the probability that the average price is between $161 and $167. \(\_\_\_\_\_\_\_\_\) c. Find the 95th percentile for the average textbook price for this sample size. \(\_\_\_\_\_\_\) (round to the nearest cent) d. Find the 95th percentile for an individual textbook price. (round to the nearest cent) \(\_\_\_\_\_\_\) e. For part b), is the assumption that the distribution is normal necessary? Yes \(\bigcirc\) No \(\bigcirc\) **Note:** - \(\bar{x}\) represents the sample mean. - Assume normal distribution due to the Central Limit Theorem if necessary.
Transcribed Image Text:**Problem Statement:** The average price of a college math textbook is $162 and the standard deviation is $27. Suppose that 10 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. **Questions:** a. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\_\_, \_\_\_\_\_\_)\) b. For the group of 10, find the probability that the average price is between $161 and $167. \(\_\_\_\_\_\_\_\_\) c. Find the 95th percentile for the average textbook price for this sample size. \(\_\_\_\_\_\_\) (round to the nearest cent) d. Find the 95th percentile for an individual textbook price. (round to the nearest cent) \(\_\_\_\_\_\_\) e. For part b), is the assumption that the distribution is normal necessary? Yes \(\bigcirc\) No \(\bigcirc\) **Note:** - \(\bar{x}\) represents the sample mean. - Assume normal distribution due to the Central Limit Theorem if necessary.
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