Sports and Leisure
The Daytona 500, often referred to as The Great American Race, is a spectacular sporting event, complete with a pre-race show. Jimmie Johnson won this race in 2013, when the mean speed per lap for all racers was 159.25 mph.13 Assume the speed is normally distributed with a standard deviation of 16 mph, and a driver and lap are selected at random.
a. What is the probability that the speed on this lap is less than 155 mph?
b. What is the probability that the speed on this lap is between 140 and 150 mph?
c. The fastest recorded speed is 212 mph at Talladega in 1986. What is the probability that the speed on this lap will set a new record?
d. What is the probability that the four leaders will all have a speed of at least 165 on this lap?