Question

An elevator has a placard stating that the maximum capacity is 2550 lb —15 passengers.​ So,15 adult male passengers can have a mean weight of up to 2550/15=170 pounds. If the elevator is loaded with 15 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 172 lb and a standard deviation of 26 lb​.)

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.​No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.

B.​Yes, 15 randomly selected people will always be under the weight limit.

C.​Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity.

D.​No, 15 randomly selected people will never be under the weight limit.

Answer 1

Let X be the weight of a random male.

X ~ N(172, 26)

Standard error of mean = = 26 / = 6.713171

Probability that it is overloaded because they have a mean weight greater than 170 lb

= P( > 170)

= P[Z > (170 - 172) / 6.713171]

= P[Z > -0.30]

= 0.6179

The probability the elevator is overloaded is 0.6179

Since the probability the elevator is overloaded is not very low, the elevator does not appears to be​ safe.

A.​No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.