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.
a. For a randomly selected woman, find the probability that her sitting eye height is less than 700 mm.
The probability that a woman's sitting eye height is less than 700mm is .1190
b. For 50 randomly selected women, what is the probability that their mean sitting height is less than 730mm?
c. When designing movie theatres with stadium seating, which result is more relevant: the probability from part (a) or part (b)?
d. Find P90, the eye height separating the bottom 90% from the top 10%.