Problem
The average price of a college math textbook is $\$ 177$ and the standard deviation is $\$ 30$. Suppose that 41 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of $x ? x-N(177$ b. For the group of 41 , find the probability that the average price is between $\$ 181$ and $\$ 187$. c. Find the first 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? o No Yes
Solution
Step 1 ：The distribution of x is given as a normal distribution with a mean of $177 and a standard deviation of $30. This is denoted as N(177, 30).
Step 2 ：Final Answer: The distribution of x is \(\boxed{N(177, 30)}\).
