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 between 8 and 9 minutes? 0.7036 0.7542 0.4492 0.2834

Explanation:

Step1: Calculate the z - scores

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 8.25\) (mean) and \(\sigma=0.4\) (standard deviation).
For \(x = 8\):
\(z_1=\frac{8 - 8.25}{0.4}=\frac{- 0.25}{0.4}=-0.625\)
For \(x = 9\):
\(z_2=\frac{9 - 8.25}{0.4}=\frac{0.75}{0.4}=1.875\)

Step2: Use the standard normal distribution table

We want to find \(P(-0.625<Z<1.875)\)
\(P(-0.625 < Z<1.875)=P(Z < 1.875)-P(Z<-0.625)\)
From the standard normal table:
\(P(Z < 1.875)\approx0.9696\)
\(P(Z<-0.625)\approx0.2660\)

Step3: Calculate the probability

\(P(-0.625 < Z<1.875)=0.9696 - 0.2660=0.7036\)

Answer:

0.7036