When designing a movie theater with stadium seating, engineers considered the si

Question

When designing a movie theater with stadium seating, engineers considered the sitting eye heights of women. These heights have a mean of 739 mm and a standard deviation of 33 mm and are normally distributed.

a. Find the probability that a randomly selected woman has a sitting eye height less than 700 mm.

b. Find the percentage of women who have a mean eye height greater than 750 mm.

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

Please provide details, so I can understand your solution. I will rate lifesaver. Thanks.

Explanation / Answer

a) Pr[x < 700] = Pr[z < (700-739)/33] = Pr[z < -1.18] = 0.1190 b) Pr[x > 750] = Pr[z > (750-739)/33] = Pr[z > 0.33] = 1 - 0.6293 = 0.3707 c) Pr[x < 730] = Pr[z > (730-739)/(33/sqrt(50)] = Pr[z < -1.93] = 0.0268

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