The median of any normal distribution is the same as its mean. We can use normal calculations to find the quartiles and related descriptive measures for normal calculations.

a. (2 points) What is the area under the standard normal curve to the left of the third quartile? Use this to find the z-score of the third quartile for a standard normal distribution. Find the area and the z-score of the first quartile similarly.

b. (3 points) Your work in (a) gives the z-scores for the quartiles of any normal distribution. The height of men in the US varies according to an approximately normal distribution with mean of 69 inches and standard deviation of 4 inches. What are the values of quartiles Q1 and Q3 of the distribution of heights of US females (in inches)?