Question

a kayak - rental company needs to replace many of its kayaks, and it wants to ensure it has enough kayaks to meet the demand from customers during the summer season. on average, it rents out 42 kayaks each day with a standard deviation of 4. the company has 45 kayaks. use a calculator to find the probability that the company will have enough kayaks on any given day. (1 point)
91.3
97
96.2
88.1

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 45\) (number of kayaks available), \(\mu=42\) (mean number of kayaks rented), and \(\sigma = 4\) (standard deviation).

$$z=\frac{45 - 42}{4}=\frac{3}{4}=0.75$$

Step2: Find the probability using the z - table

We want to find \(P(X\leq45)\). Looking up the z - score of \(z = 0.75\) in the standard normal table (z - table). The value corresponding to \(z = 0.75\) is \(0.7734\approx77.3\%\)

Answer:

77.3