Question

An elevator has a placard stating that the maximum capacity is 1304 lb long dash—88 passengers.​ So, 88 adult male passengers can have a mean weight of up to 1304 divided by 8 equals 163 pounds.1304/8=163 pounds. If the elevator is loaded with 88 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 163 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 be​ safe?

Answer 1

Solution :

Given that,

mean = = 170

standard deviation = = 32

n = 8

= = 170

= / n = 32 / 8 = 11.31

P( > 163) = 1 - P( < 163)

= 1 - P[( - ) / < (163 - 170) / 11.31 ]

= 1 - P(z < -0.62 )

Using z table,    

= 1 - 0.2676

= 0.7324

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