Question

the amount of time it takes an athlete to complete a ninja warrior course is normally distributed with mean 8.25 minutes and standard deviation 0.4 minutes. the fastest 5% of athletes to complete the course are invited to attend a regional competition. what is the cutoff time to be invited to regionals? 8.25 minutes 8.91 minutes 7.59 minutes 7.84 minutes

Explanation:

Step1: Find the z - score

Since we want the fastest 5% (i.e., the lower 5% of the normal distribution), we look up the z - score in the standard normal distribution table. The z - score corresponding to an area of 0.05 is approximately \(z=-1.645\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 8.25\) (mean), \(\sigma=0.4\) (standard deviation), and \(z=-1.645\).
We solve for \(x\):

$$
LATEXBLOCK0
$$

Answer:

7.59 minutes