A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 22 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage less than 21 mpg. Round your answer to four decimal places.
A)0.4013
B)0.9013
C)0.0987
D)0.5987
E)0.1974

Question

A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 22 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage less than 21 mpg. Round your answer to four decimal places. ​
A)0.4013
B)0.9013
C)0.0987
D)0.5987
E)0.1974

Quizplus · Accepted Answer

To find the probability that a car has gas mileage less than 21 mpg, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (21 mpg), μ is the mean (22 mpg), and σ is the standard deviation (4 mpg). Plugging in the values, we get Z = (21 - 22) / 4 = -0.25. Looking up -0.25 on the standard normal distribution table or using a calculator gives us a probability of approximately 0.4013.

A Certain Model of Automobile Has Its Gas Mileage (In