Elementary statistics

Question

An elevator has a placard starting that the maximum capacity is 1680 lb- 10 passengers. So, 10 adult male passengers can have a mean weight of up to 1680/10=168 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that is overloaded because they have a mean weight greater than 168 lb. (assume that weights of males are normally distributed with a mean of 175 lb and a standard deviation of 25 lb.) does this elevator appear to be safe?

probability the elevator is overloaded?

Answer 1

µ = 175 lb.

σ = 25 lb.

X = 168 lb.

n = 10 adult male passengers

Set up the z-score formula.

z = (X - μ) / (σ/√n) = (168 - 175) / (25/√10) = -0.89

P(z > -0.89) = 1 - P(z ≤ -0.89) = 1 - 0.1867 = 0.8133

The probability that the elevator is overloaded because the mean weight is greater than 168 lb. is 0.8133. In this case, the elevator is not safe to ride on.