Question

An elevator has a placard stating that the maximum capacity is 1360 lb-8 passengers. So, 8 adult male passengers can have a mean weight of up to 1360/8 170 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 170 lb. (Assume that weights of males are normally distributed with a mean of 175 lb and a standard deviation of 30 Ib.) Does this elevator appear to be safe? 

The probability the elevator is overloaded is _______ Round to four decimal places as needed.) 

Does this elevator appear to be safe? 

A. Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity 

B. Yes, 8 randomly selected people will always be under the weight limit.

C. No, there is a good chance that 8 randomly selected people will exceed the elevator capacity 

D. No, 8 randomly selected people will never be under the weight limit.

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	175
std deviation   =σ=	30.0000
sample size       =n=	8
std error=σx̅=σ/√n=	10.6066

probability =

P(X>170)

=

P(Z>-0.47)=

1-P(Z<-0.47)=

1-0.3192=

0.6808

option C is correct