The average price of a college math textbook is $169 and the standard deviation is $24. Suppose that 16 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of xx? xx ~ N(,)
2. For the group of 16, find the probability that the average price is between $166 and $174.
3. Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)
4. For part b), is the assumption that the distribution is normal necessary? YesNo