Question

Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in less than 188 minutes?

Answer 1

Answer:

0.53983.

Step-by-step explanation:

We have been given that  x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes.

First of all, we will find z-score of random sample score 188 using z-score formula.

$z=\frac{x-\mu}{\sigma}$, where,

z = Z-score,

x = Random sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{188-190}{21}$

$z=\frac{-2}{21}$

$z=-0.095238095$

$z\approx -0.10$

Now, we will use normal distribution table to find the probability that this runner will complete this road race in less than 188 minutes as:

$P(z<-.10)=0.53983$

Therefore, the probability that one runner will complete the road race in less than 188 minutes is 0.53983.