Chapter 6.4, Problem 10BSC

Elevator Safety Exercise 9 uses μ = 189 lb, which is based on Data Set 1 “Body Data” in Appendix B. Repeat Exercise 9 using μ = 174 lb (instead of 189 lb), which is the assumed mean weight that was commonly used just a few years ago. What do you conclude about the effect of using an outdated mean that is substantially lower than it should be?

9. Elevator Safety Example 2 referred to an elevator with a maximum capacity of 4000 lb. When rating elevators, it is common to use a 25% safety factor, so the elevator should actually be able to carry a load that is 25% greater than the stated limit. The maximum capacity of 4000 lb becomes 5000 lb after it is increased by 25%, so 27 adult male passengers can have a mean weight of up to 185 lb. If the elevator is loaded with 27 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 185 lb. (As in Example 2, assume that weights of males are normally distributed with a mean of 189 lb and a standard deviation of 39 lb.) Does this elevator appear to be safe?