The capacity of an elevator is 10 people or 1670 pounds The

The capacity of an elevator is 10 people or 1670 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than1670/10=167 pounds.Suppose the people have weights that are normally distributed with a mean of 176 lb and a standard deviation of 35 lb.

(a) Find the probability that if a person is randomly selected, his weight will be greater than167 pounds.The probability is approximately(__)

(Round to four decimal places as needed.)

(b) Find the probability that 10 randomly selected people will have a mean that is greater than167 pounds.The probability is approximately nothing.

(Round to four decimal places as needed.)

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

A. Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.

B. No, 10 randomly selected people will never be under the weight limit.

C. Yes, 10 randomly selected people will always be under the weight limit.

D. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

Solution

Mean ( u ) =176
Standard Deviation ( sd )=35
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 167) = (167-176)/35
= -9/35 = -0.2571
= P ( Z >-0.257) From Standard Normal Table
= 0.6015                  
b)
P(X > 167) = (167-176)/35/ Sqrt ( 10 )
= -9/11.068= -0.8132
= P ( Z >-0.8132) From Standard Normal Table
= 0.7919                  
c)
A. Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.