Paxton Hoffman

2022-07-18

You are interested in finding how many hours a person is willing to wait for a plane. It is found that the time people are willing to wait has a $\mu =5.2$ and a $\sigma =1.1$. What is the probability a person is willing to wait more than seven hours?
Using the standard score formula, $z=\left(x-\mu \right)/\sigma$, the z-score equals to two decimal places 1.64, which corresponds to a probability of 0.9495 on my z-score tables. However, on the answer key provided, it states the probability is 0.0505 or what would correspond to a z-score of −1.64.
Is this a trick of the wording involved in the question or are my z-tables (or standard score formula) wrong?

tykoyz

Expert

You've computed correctly, but interpreted the number incorrectly. What you've found is the probability that someone is willing to wait at most 7 hours; the probability you want is
$1-0.9495=0.0505$