Question

5. The capacity of an elevator is 10 people or 1660 pounds. The capacity will be exceeded if 10 people have weights with a mean greater than 1660/10=166 pounds. Suppose the people have weights that are normally distributed with a mean of 176 lb and a standard deviation of 30 lb.

a. Find the probability that if a person is randomly​ selected, his weight will be greater than 166 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 than 169 pounds. The probability is approximately______(Round to four decimal places as​ needed.)

C. Does the elevator appear to have the correct weight​ limit? Why or why​ not?

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

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

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

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

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	176
std deviation   =σ=	30.0000

probability =

P(X>166)

=

P(Z>-0.33)=

1-P(Z<-0.33)=

1-0.3707=

0.6293

b)

sample size       =n=	10
std error=σx̅=σ/√n=	9.4868

probability =

P(X>169)

=

P(Z>-0.74)=

1-P(Z<-0.74)=

1-0.2296=

0.7704

c)

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