Answer to Question #150597 in Statistics and Probability for Vladimyr Lubin

Question #150597

(6.4.9) An elevator has a placard stating that the maximum capacity is 1240 lb 8 passengers. So, adult male passengers can have a mean weight of up to 1240/8=155 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 155lb. (Assume that weights of males are normally distributed with a mean of 163 Ib and a standard deviation of 33 Ib.) Does this elevator appear to be safe?
The probability the elevator is overloaded is

Expert's answer

z = (X - μ)/σ = (155-163)/33 = -0.2424

P(x>z) = 0.5958

Answer: 0.5958

This elevator does not appear to be safe.