A certain type of elevator has a maximum weight capacity X w

A certain type of elevator has a maximum weight capacity X, which is normally distributed with a mean and a standard deviation of 5000 and 300 pounds, respectively. For a certain building equipped with this type of elevator, the elevator loading Y is a normally distributed random variable with a mean and a standard deviation of 4000 and 400 pounds, respectively. For any given time that the elevator is in use, find the probability that it will be overloaded, assuming that X and Y are independent.

Solution

A certain type of elevator has a maximum weight capacity X where X~N(5000,300²)

For a certain building equipped with this type of elevator, the elevator loading Y~N(4000,400²)

[Since X and Y are independent,Y-X~N(-1000,500²)]

For any given time that the elevator is in use, find the probability that it will be overloaded=P(Y>X)=P(Y-X>0)

=1-P(Y-X<=0)=1-0.977250=0.0227500