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

The given parameters are:

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

Calculating the z score using:

`z=(x-\mu)/(\sigma)`

This gives:

`\begin{gathered} z=(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.