The capacity of an elevator is 10 people or 1630 pounds The

The capacity of an elevator is 10 people or 1630 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1630/10=163 pounds.

Suppose the people have weights that are normally distributed with a mean of 168 lb and a standard deviation of 26 lb.

(a) Find the probability that if a person is randomly selected, his weight will be greater than 163 pounds. (Round to four decimal places as needed.)

(b) Find the probability that 8 randomly selected people will have a mean that is greater than 163 pounds.

(c) Does the elevator appear to have the correct weight limit? Why or why not?

Solution

Capcity of elevator = 1630 pounds

Weight of any person is normal (168, 26)

a) P(X>163) = P(Z>-5/26)

= P(Z>-0.19) = 0.5753

b) When n =8

std error = 26/rt8 = 9.192

P(X>163) = P(Z>-5/9.192)

= P(Z>-0.54)

= 0.7088

c) For checking this let us consider sample of 10 persons

n =10

Std error = 26/rt10

= 8.2

P(X>163)

= P(z>-5/8.2)

= P(z>-0.61)

= 0.7291

No, the elevator does not appear to have correct weight limit

As prob for any random sample exceeding the prescribed weight = 0.7291 very high.