Question

For a car traveling 40 miles per hour (mph), the distance required to brake to a stop is normally distributed with a mean of 140 feet and a standard deviation of 16 feet. Suppose you are traveling 40 mph in a residential area and a car moves abruptly into your path at a distance of 168 feet. (Round your answers to four decimal places.)

(a)

If you apply your brakes, what is the probability that you will brake to a stop within 112 feet or less?

If you apply your brakes, what is the probability that you will brake to a stop within 140 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?

Answer 1

To answer this question, we can use the concept of the normal distribution to calculate the probabilities of braking to a stop within certain distances and avoiding a collision.

Step-by-step explanation:

To answer this question, we can use the concept of the normal distribution. Given that the distance required to brake to a stop is normally distributed with a mean of 140 feet and a standard deviation of 16 feet, we can calculate the probabilities.

(a) To find the probability of braking to a stop within 112 feet or less, we need to calculate the z-score for 112 feet using the formula z = (x - mean) / standard deviation. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the corresponding probability. Repeat this process to find the probability of braking to a stop within 140 feet or less.

(b) To find the probability of avoiding a collision by braking to a stop, we need to calculate the z-score for 168 feet (distance of the car moving abruptly into your path) using the same formula. Then, we can use the standard normal distribution table or a calculator to find the probability of braking to a stop within that distance.