Question

Assume that the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62mph and a standard deviation of 10 mph. If 300 cars are selected at random, how many will be traveling slower than 45 mph?

a) 45 cars
b) 90 cars
c) 120 cars
d) 150 cars

Answer 1

To find the number of cars traveling slower than 45 mph out of 300 cars, we need to calculate the probability and multiply it by the total number of cars. The answer is approximately 13 cars.

Step-by-step explanation:

To find the number of cars traveling slower than 45 mph, we need to calculate the probability that a car randomly selected from the 300 cars will have a speed below 45 mph. First, we need to standardize the value of 45 mph by subtracting the mean and dividing by the standard deviation. This gives us a z-score of:

z = (45 - 62) / 10 = -1.7

Next, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.7. The probability is approximately 0.0446 or 4.46%. Finally, we can multiply this probability by the total number of cars (300) to find the number of cars traveling slower than 45 mph:

Number of cars = Probability * Total cars = 0.0446 * 300 = 13.38 ≈ 13 cars

Therefore, the correct answer is option a) 45 cars.