Question

The weights of the packages received by a department store have a mean of 300 lb and a standard deviation of 50 lb. What is the probability that 25 packages received at random and loaded on an elevator will exceed the safety limit of the elevator, listed as 8,200 lb?

Answer 1

Let, X : weight of 25 packages.

Mean = 25 x 300 = 7500 and

SD = 300 x sqrt(25) = 1500

X follows Normal(7500 , 1500)

Z = (X - 7500)/1500 = (8200-7500)/1500= 0.47

P(X > 8200) = 1 - P(Z < 0.47) = 1 - 0.6796 = 0.3204