Question

12. The elevator in the car rental building at San Francisco International airport has a placard stating that the max capacity is 4000lb _ 27passengers. Because 4000/27=148, this converts to a mean passenger weight of 148lb when the elevator is full. Assuming that elevator is filled with 27 adult males and adult males’ weights are normally distributed with a mean of 189lb and standard deviation of 39lb

a. Find the probability that 1 randomly selected adult male has a weight greater than 148lb.

b. Find the probability that a sample of 27 randomly selected adult males has a mean weights greater than 148lb.

Answer 1

Solution :

Given that ,

a) P(x > 148) = 1 - p( x< 148)

=1- p P[(x - ) / < (148 - 189) / 39]

=1- P(z < -1.05)

= 1 - 0.1469

= 0.8531

b) = 189

= / n = 39 / 27 = 7.51

P( > 148) = 1 - P( < 148)

= 1 - P[( - ) / < (148 - 189) / 7.51]

= 1 - P(z < -5.46)   

= 1 - 0

= 1