Question

Suppose you must establish regulations concerning the maximum number of people who can occupy an elevator. A study of elevator occupancies indicates that, if eight people occupy the elevator, the probability distribution of the total weight of the eight people has a mean equal to 1,200 pounds and a variance equal to 9,800 lbs2. Assume that the probability distribution is approximately normal. We are interested in the probability of exceeding 1,300 in the elevator.

The Z value for this problem is:

o 1.01

o 3.03

o 2.02

o None of the others

Answer 1

Solution :

Given that ,

mean = = 1200

variance = ² = 9800

standard deviation =  = ² = 9800 = 99

x = 1300

Using z-score formula,

z = x - /   

z = 1300 - 1200 / 99

z = 1.01

P(z > 1.01)

=1- P(z < 1.01)

= 1 - 0.8438

Probability = 0.1562