a. What is the distribution of ? a - N( b. For the group of 44, find the probability that the average price is between $173 and $178. c. Find the third quartile for the average textbook price for this sample size. $ (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? No Yes

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The average price of a college math textbook is $167, and the standard deviation is $28. Suppose that 44 textbooks are randomly chosen. Round all answers to four decimal places where possible.

a. What is the distribution of \( \overline{x} \)? \(\overline{x} \sim N(\, \_\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_\_ \,)\)

b. For the group of 44, find the probability that the average price is between $173 and $178. \[\_\_\_\_\_\_\_\_\_\_\_\]

c. Find the third quartile for the average textbook price for this sample size. $[\_\_\_\_\_\_\_\_\_\_\_\] (round to the nearest cent)

d. For part b), is the assumption that the distribution is normal necessary?  
[ ] No   
[ ] Yes
Transcribed Image Text:The average price of a college math textbook is $167, and the standard deviation is $28. Suppose that 44 textbooks are randomly chosen. Round all answers to four decimal places where possible. a. What is the distribution of \( \overline{x} \)? \(\overline{x} \sim N(\, \_\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_\_ \,)\) b. For the group of 44, find the probability that the average price is between $173 and $178. \[\_\_\_\_\_\_\_\_\_\_\_\] c. Find the third quartile for the average textbook price for this sample size. $[\_\_\_\_\_\_\_\_\_\_\_\] (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? [ ] No [ ] Yes
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