Question

Peter has collected data to find that the finishing times for cyclists in a race has a normal distribution. Based on the Empirical Rule, what is the probability that a randomly selected race participant had a finishing time of greater than 171 minutes if the mean is 156 minutes and the standard deviation is 15 minutes? Enter your answer as a percent rounded to 2 decimal places if necessary. Include the percent symbol % in your answer.

Answer 1

Given,

= 156 , = 15

z = (X - ) /

= (171 -156) / 15

= 1

That is score 171 is 1 standard deviation above the mean.

According to empirical rule, approximately 68% of the data falls between 1 standard deviation of the mean.

So, 32% (1 - 68%) outside the 1 standard deviation of the mean and 16% to each side.

Therefore,

P(X > 171) = 16%