Watersports Rental at Flathead Lake rents jet skis and power boats for day use. Each piece of equipment has a clock that records the time that it was actually in use while rented. The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours. Watersports management has decided to give a rebate to customers who use the equipment for less than 2.0 hours. Based on this information, the probability that a customer will get the rebate is 0.4082.

Question

Quizplus · Accepted Answer

To find the probability that a customer will get a rebate (i.e., use the equipment for less than 2.0 hours), we need to calculate the z-score for 2.0 hours and then find the corresponding probability from the standard normal distribution. The z-score is calculated as $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value of interest (2.0 hours), $\mu$ is the mean (3.6 hours), and $\sigma$ is the standard deviation (1.2 hours). Plugging in the values, we get $z = \frac{(2.0 - 3.6)}{1.2} = -1.33$. Looking up the z-score of -1.33 in a standard normal distribution table or using a calculator gives a probability of approximately 0.0918, not 0.4082. This means the probability that a customer will use the equipment for less than 2.0 hours (and thus get a rebate) is about 9.18%, not 40.82%.

Watersports Rental at Flathead Lake Rents Jet Skis and Power