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.
what proportion of athletes complete the course in more than 9 minutes?
0.0304 0.1342
0.9696 0.8658

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 9\), \(\mu=8.25\), and \(\sigma = 0.4\).

$$z=\frac{9 - 8.25}{0.4}=\frac{0.75}{0.4}=1.875$$

Step2: Find the proportion

We want \(P(X>9)\), which is equivalent to \(P(Z>1.875)\). Since \(P(Z > z)=1 - P(Z\leq z)\), and looking up \(P(Z\leq1.875)\) in the standard normal table (or using a calculator with a normal - distribution function). Using a calculator, \(P(Z\leq1.875)\approx0.9696\). Then \(P(Z>1.875)=1 - 0.9696 = 0.0304\)

Answer:

0.0304