# Normal distribution

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2. In the Boston Marathon each April there are approximately 100 male runners who participate and who are considered as world class runners. It is known that the time they require to finish the 26.2 mile race is normally distributed with a mean of 135.45 minutes and a standard deviation of 2.30 minutes. If a world class runner takes more than 141 minutes before crossing the finish line then they are automatically removed from world-class status. What is the probability that a randomly selected world class runner will be removed from world class status?

Choose one answer.

a. 0.9920

b. 0.0184

c. 0.9816

d. 0.0080

e. none of these

9. A local track club has decided to sponsor a 10,000-meter road race. From past results of races across the state, it is known that the length of time to complete the race has an approximately normal distribution with a mean of 56.72 minutes and a standard deviation of 7 minutes. The club has decided that every person that finishes the race under 64 minutes will receive a medal. What percentage of racers will receive a medal? Round your answer to the nearest percentage.

Choose one answer.

a. 15%

b. 22%

c. 78%

d. 85%

e. 100%

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#### Solution Summary

This solution is an example of how to calculate probability when working with a normal distribution.