Question

Assume that the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 67 mph and a standard deviation of 5 mph. What percent of cars are traveling faster than 75 mph?

Answer 1

Approximately 5.48% of cars are traveling faster than 75 mph during rush hour on the expressway.

Step-by-step explanation:

We are given that the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 67 mph and a standard deviation of 5 mph. We want to find the percent of cars that are traveling faster than 75 mph.

To find this, we need to calculate the z-score for 75 mph using the formula:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z = (75 - 67) / 5 = 1.6

We can then use a z-table or calculator to find the area to the right of the z-score of 1.6, which represents the percentage of cars traveling faster than 75 mph. From the z-table, we find that the area to the right of 1.6 is approximately 0.0548, or 5.48%.

Therefore, approximately 5.48% of cars are traveling faster than 75 mph during rush hour on the expressway.