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4. (20 points) Completion times...

4. (20 points) Completion times of a popular marathon race are approximately Normally distributed with a mean of 230 minutes and a standard deviation of 23 minutes.(a.) Find the probability that a randomly selected runner will take from 3 hours and 30 minutes to 4 hours and 10 minutes to finish the race.

(b.) Find the probability that such a runner will complete the race in under 2 hours and 50 minutes?

(c.) If a runner finishes the race in under 3 hours, what is the probability that runner will finish the race in under 2 hours and 50 minutes?

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