A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 40 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage greater than 50 mpg. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places.
A)0.9938
B)0.0062
C)0.9907
D)0.4938
E)0.0169

Question

A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 40 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage greater than 50 mpg. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​
A)​0.9938
B)​0.0062
C)​0.9907
D)​0.4938
E)​0.0169

Quizplus · Accepted Answer

We need to standardize the given value of 50 mpg using the formula z = (x - mu) / sigma, where x is the given value, mu is the mean, and sigma is the standard deviation. Thus, z = (50 - 40) / 4 = 2.5. Using a standard normal distribution table, we can find that the probability of a randomly selected car having a gas mileage greater than 50 mpg is approximately 0.0062, which corresponds to the area to the right of z = 2.5. Therefore, the correct answer is B.

A Certain Model of Automobile Has Its Gas Mileage (In