The average price of a college math textbook is $150 and the standard deviation is $27. Suppose that 49 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
a. What is the distribution of $\bar{x}$? $\bar{x}$ ~ N(150, 3.8571)
b. For the group of 49, find the probability that the average price is between $145 and $150.
c. Find the first quartile for the average textbook price for this sample size. $ (round to the nearest cent)