Question

An elevator has a placard stating that the maximum capacity is 2310 lblong dash15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2310 divided by 15 equals 154 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 154 lb.​ (Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 35 lb​.) Does this elevator appear to be​ safe? The probability the elevator is overloaded is?

Answer 1

Solution :

Given that,

mean = = 161

standard deviation = = 35

n = 15

=   = 161

= / n = 35 / 15 = 9.04

P( > 154) = 1 - P( < 154 )

= 1 - P[( - ) / < (154 - 161) / 9.04]

= 1 - P(z < - 0.77)

Using z table,    

= 1 - 0.2206

= 0.7794

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