Question

Assume that the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 61 mph and a standard deviation of 10 mph. If 300 cars are selected at random, how many will be traveling slower than 45 mph?

a) Approximately 66 cars

b) Approximately 84 cars

c) Approximately 16 cars

d) Approximately 114 cars

Answer 1

To find the number of cars traveling slower than 45 mph out of 300 cars with a normal distribution, we need to calculate the z-score of 45 and find the corresponding probability. The number of cars will be this probability multiplied by 300, which is approximately 16.

Step-by-step explanation:

To find the number of cars that will be traveling slower than 45 mph, we need to calculate the z-score of 45 using the formula: z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (45 - 61) / 10 = -1.6.

Lookup the z-score in the z-table or use a calculator to find the probability corresponding to the z-score. The probability of a car traveling slower than 45 mph is approximately 0.0548.

To find the number of cars, multiply the probability by the total number of cars, which is 300.

So, the number of cars traveling slower than 45 mph is approximately 0.0548 * 300 = 16.44, which we can round to 16.