Question

An elevator has a placard stating that the maximum capacity is 1328 lb—8 passengers. So, 8 adult male passengers can have a mean weight of up to 1328/8=166 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 166 lb. (Assume that weights of males are normally distributed with a mean of 169 lb and a standard deviation of 35 lb.) Does this elevator appear to be safe?

Answer 1

SOLUTION:

The given parameters are:

$x=166,\mu=169,\sigma=35$

Calculating the z score using:

$z=\frac{x-\mu}{\sigma}$

This gives:

$\begin{gathered} z=\frac{166-169}{35} \\ z=-0.086 \end{gathered}$

The probability is given as:

$P(z>-0.086)=0.53427$

Therefore the probability that the weight is overloaded is 0.53427

Therefore the correct option is B.