6.22 Braking Distances For a car travelling 50 kilometres per hour (km/h), the distance required to brake to a stop is normally distributed with a mean of 15 metres (m) and a standard deviation of 2.5 m. Suppose you are travelling 50 km/h in a residential area and a car moves abruptly into your path at a distance of 18 m.

a. If you apply your brakes, what is the probability that you will brake to a stop within 12 m or less? Within 15 m 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?