Question

2. the completion times to run a road race are normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. a) what is the probability that a randomly selected runner will finish the race in less than 150 minutes? (around your answer to 4 decimal places)

Answer 1

0.0287

Explanation:

we first of all need to find the z-score.

z = (X - υ) / σ

where X is the test statistic, υ is the mean and is the standard deviation.

z = (150 - 190) / 21

= -1.9047....

in z-table, the value of the area for z = -1.9047 is 0.02872.

this is the area to the left (finishing race in less than 150 minutes).

so the probability is 0.02872 = 0.0287 to 4 decimal places