Question

An elevator has a placard stating that the maximum capacity is 1328 lb--8 passengers. So, 8 adult male passengers can have a mean weight of up to 1328/8=166 pounds. If the elevator is loaded with 8 male passengers, find the probability that it is overloaded because they have a mean weight greater than 166 lb. (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 29 lb.) Does this elevator appear to be safe?

Answer 1

Solution :

Given that,

mean = = 173

standard deviation = = 29

n = 8

=   = 173

= / n = 29 / 8 = 10.25

P( > 166) = 1 - P( < 166)

= 1 - P[( - ) / < (166 - 173) /10.25 ]

= 1 - P(z < -0.68)

Using z table,    

= 1 - 0.2483

= 0.7517

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