Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds follow an approximately Normal distribution with mean 115 miles per hour (mph) and standard deviation 6 mph. Choose one of Djokovic’s first serves at random. Let Y = its speed, measured in miles per hour.

a. Write the event “speed is between 100 and 120 miles per hour” in terms of Y. Then find this probability.

b. Find the value of c such that P(Y ≤ c) = 0.15.