Question

An elevator has a placard stating that the maximum capacity is 1344 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1344 divided by 8 equals 168 pounds. If the elevator is loaded with 8 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb.​ (Assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 32 lb​.) Does this elevator appear to b

Answer 1

Solution :

Given that,

mean = = 170

standard deviation = = 32

n = 8

=   = 170

= / n = 32 / 8 = 11.31

P( > 168) = 1 - P( < 168)

= 1 - P[( - ) / < (168 - 170) /11.31 ]

= 1 - P(z < -0.18)

Using z table,    

= 1 - 0.4286

= 0.5714

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