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

16%

Explanation:

Emperical rule states that:

1. About 68% of data fall within 1 standard deviation of mean.

2. About 95% of data falls within 2 standard deviation of mean.

3. About 99.7% of data falls within 3 standard deviation of mean.

Let the time to finish for cyclist be y

P(y>156) = 1 - P(y < = 156)

1 - P(y - u/6 <= 171 -151)

1- P(z<=1)

156 minutes falls within 1 standard deviation, above the mean the Probability of getting more than 156mins is

1- 0.68 /2 = 0.16

0.16 ×100=16%