Question

Question 23 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. Provide your answer below:

Answer 1

According to empirical rule,

Approximately 68% data lies in one standard deviation of the mean.

That is 32% of the data lies outside 1 standard deviation of the mean and 16% to either side.

Given,

Mean = 156 , SD = 15

171 = 156 + 15

= mean + 1 * SD

171 is 1 standard deviation above the mean,

According to empirical rule,

P( X > 171) = 16%