Question

An elevator has a placard stating that the maximum capacity is

1944 lblong dash—12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 1944 divided by 12 equals 162 pounds.1944/12=162 pounds.If the elevator is loaded with 12 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 162lb.​ (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of35 lb​.) Does this elevator appear to be​ safe? The probability the elevator is overloaded is nothing.

(Round to four decimal places as​ needed.)

Does this elevator appear to be​ safe?

A.​Yes, there is a good chance that

12

randomly selected people will not exceed the elevator capacity.

B.​No, there is a good chance that

12

randomly selected people will exceed the elevator capacity.

C.​No,

12

randomly selected people will never be under the weight limit.

D.​Yes,12 randomly selected people will always be under the weight limit.

Answer 1

Solution :

Given that,

mean = = 165

standard deviation = = 35

n = 12

=   = 165

= / n = 35 / 12 = 10.1

P( > 162) = 1 - P( < 162)

= 1 - P[( - ) / < (162 - 165) / 10.1 ]

= 1 - P(z < -0.30)

Using z table,    

= 1 - 0.3821

= 0.6179

B) No, there is a good chance that 12 randomly selected people will exceed the elevator capacity.