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 percentage of athletes complete the course in less than 7.5 minutes?
3.04%
38.92%
13.42%
51.34%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 7.5\), \(\mu=8.25\), and \(\sigma = 0.4\).

$$ z=\frac{7.5 - 8.25}{0.4}=\frac{- 0.75}{0.4}=-1.875 $$

Step2: Find the probability using the standard normal distribution table

We want to find \(P(X\lt7.5)\), which is equivalent to \(P(Z\lt - 1.875)\).
Looking up the value of \(z=-1.875\) in the standard - normal distribution table (or using a calculator with a normal - distribution function, e.g., for a TI - 84: normalcdf(-100,-1.875)).
From the standard normal table, \(P(Z\lt - 1.875)\approx0.0304\)

Answer:

3.04%