When designing a movie theater with stadium seating, engineers decide to consider the sitting eye heights of women. Those heights have a mean of 739 mm and a standard deviation of 33 mm and they are normally distributed (based on anthropometric survey data from Gordon, Churchill, Clauser).

a. For a randomly selected woman, what is the probability that she has a sitting eye height less than 700 mm?

b. What percentage of women have a sitting eye height greater than 750 mm?

c. For 50 randomly selected women, what is the probability that their mean sitting height is less than 730 mm?

d. For sitting heights of women, find the value of P₉₀, which is the 90th percentile.