The speed of cars passing through a check point follows a normal distribution with a mean of 45 miles per hour and a standard deviation of 6 miles per hour.What is the probability that the next car passing will be exceeding 51 miles per hour?
A)0.9854
B)0.8413
C)0.7967
D)0.1587

Question

Quizplus · Accepted Answer

We need to find the probability of a car exceeding 51 miles per hour, which means finding the area under the normal distribution curve to the right of 51 mph. We can standardize 51 mph 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. Thus, we have:

z = (51 - 45) / 6
z = 1

Using a standard normal distribution table, we find that the area to the right of z = 1 is 0.1587. Therefore, the probability of the next car passing exceeding 51 miles per hour is 0.1587 or 15.87%, which is option D.

The Speed of Cars Passing Through a Check Point Follows