Question

The capacity of an elevator is

1212

people or

19801980

pounds. The capacity will be exceeded if

1212

people have weights with a mean greater than

1980 divided by 12 equals 165 pounds.1980/12=165 pounds.

Suppose the people have weights that are normally distributed with a mean of

168 lb168 lb

and a standard deviation of

31 lb31 lb.

a. Find the probability that if a person is randomly selected, his weight will be greater than

165165

pounds.The probability is approximately

0.53980.5398.

(Round to four decimal places as needed.)b. Find the probability that

1212

randomly selected people will have a mean that is greater than

165165

pounds.The probability is approximately

nothing.

(Round to four decimal places as needed.)

Answer 1

µ = 168

sd = 31

n = 12

                          

                           = P(Z > -0.34)

                           = 1 - P(Z < -0.34)

                           = 1 - 0.3669

                           = 0.6331