Question

The capacity of an elevator is

1010

people or

16001600

pounds. The capacity will be exceeded if

1010

people have weights with a mean greater than

1600 divided by 10 equals 160 pounds.1600/10=160 pounds.

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

162 lb162 lb

and a standard deviation of

28 lb28 lb.

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

160160

pounds.The probability is approximately

0.52830.5283.

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

1010

randomly selected people will have a mean that is greater than

160160

pounds.The probability is approximately

nothing.

(Round to four decimal places as needed.)

Answer 1

Solution :

Given that ,

mean = = 162

standard deviation = = 28

n = 10

= = 162 and

= / n = 28 / 10 = 8.85

P( > 160) = 1 - P( < 160)

= 1 - P(( - ) / < (160 - 162) / 8.85)

= 1 - P(z < -0.23)

= 1 - 0.4090

= 0.5910

Probability = 0.5910