Question

12. Disney Monorail Consider the same Mark VI monorail described in the preceding exercise.

Again assume that heights of men are normally distributed with a mean of 68.6 in. and a

standard deviation of 2.8 in.

a. In determining the suitability of the monorail door height, why does it make sense to consider

men while women are ignored?

b. Mark VI monorail cars have a capacity of 60 passengers. If a car is loaded with 60 randomly

selected men, what is the probability that their mean height is less than 72 in.?

c. Why can’t the result from part (b) be used to determine how well the doorway height

accommodates men?

Answer 1

a) Generally we consider that the heights of men are greater than the heights of women.So in determining the suitability of the monorail door height, it makes sense to consider the heights of men.

b) P( < 72)

= P(( - )/() < (72 - )/())

= P(Z < (72 - 68.6)/(2.8/))

= P(Z < 9.41)

= 1

c) Since the probability in part b is greater than 0.95, so it will be unusual. So it cannot be used to determine how well the doorway height accommodates men.