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When designing a movie theater with stadium seating, engineers decide to consider the sitting eye heights of women.

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. What percentage of women has a sitting eye height greater than 750 mm?
c. If fifty women are randomly selected, find the probability that their mean sitting eye height is less than 730mm.
d. Find P90, the eye height separating the bottom 90% from the top 10%.

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