Assume that gas mileage for cars is normally distributed with a mean of 23.5 miles per gallon and a standard deviation of 10 miles per gallon. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is the probability that a randomly selected car gets between 15 and 30 miles per gallon? (Round the answer to 4 decimal places)

(b) Find the 75th percentile of the gas mileage distribution. (Round the answer to 2 decimal places)

14. Based on the performance of all individuals who tested between 2015 and 2017, the GMAT total scores are normally distributed with a mean of 561.27 and a standard deviation of 119.31. Show all work. Just the answer, without supporting work, will receive no credit.

(a) For a sample of size 100, state the standard deviation of the sample mean (the "standard error of the mean"). (Round your answer to three decimal places)

(b) Suppose a sample of size 100 is taken. Find the probability that the sample mean GMAT total scores is more than 575. (Round your answer to three decimal places)