Question

An elevator has a placard stating that the maximum capacity is 2565 lb/15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2565 divided by 15 equals 171 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 171 lb.​ (Assume that weights of males are normally distributed with a mean of 179 lb and a standard deviation of 27 lb ​.) Does this elevator appear to be​ safe?

Answer 1

Solution :

Given that,

mean = = 179

standard deviation = = 27

n = 15

=   = 179

= / n =27 / 15 = 6.97

P( > 171 ) = 1 - P( < 171)

= 1 - P[( - ) / < (171 - 179) / 6.97 ]

= 1 - P(z < - 1.15)

Using z table,    

= 1 - 1251

= 0.8749

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