Question

An elevator has a placard stating that the maximum capacity is 1560 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1560/10=156 pounds. If the elevator is loaded with

10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 156 lb.​ (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 28 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. Yes, 10 randomly selected people will always be under the weight limit.

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

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

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

Answer 1

Solution :

Given that,

mean = = 165

standard deviation = = 28

n = 10

= = 165

= / n = 28 / 10 = 8.85

P( > 156) = 1 - P( < 156)

= 1 - P[( - ) / < (156 - 165) /8.85 ]

= 1 - P(z < -1.02 )

Using z table,    

= 1 - 0.1539

= 0.8461

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