For a car traveling 30 miles per hour (mph), the distance required to brake to a stop is normally distributed with a mean of 50 feet and a standard deviation of 8 feet. Suppose you are traveling 30 mph in a residential area and a car moves abruptly into your path at a distance of 60 feet.
a. If you apply your brakes, what is the probability that you will brake to a stop within 40 feet or less? Within 50 feet or less?
b. If the only way to avoid a collision is to brake to a stop, what is the probability that you will avoid the collision?