Question

A certain model of car has a highway gas

mileage with a mean of 28.45 mpg and a standard
deviation of 0.32 mpg. Assume the highway gas mileage
of these cars is normally distributed.

a.) If one of these cars is randomly selected, find the probability
that the car’s gas highway mileage is greater than 28.3 mpg.

Answer 1

To find the probability that the car's highway mileage is greater than 28.3 mpg, calculate the z-score for this value and find the area under the normal distribution curve. Subtract this area from 1 to get the probability.

Step-by-step explanation:

To find the probability that the car's highway mileage is greater than 28.3 mpg, we need to calculate the z-score for this value and then find the area under the normal distribution curve to the right of this z-score.

The formula to calculate the z-score is:

z = (x - μ) / σ

Where:

• z is the z-score
• x is the value we want to calculate the probability for
• μ is the mean of the population
• σ is the standard deviation of the population

Plugging in the values:

• x = 28.3 mpg
• μ = 28.45 mpg
• σ = 0.32 mpg

z = (28.3 - 28.45) / 0.32 = -0.15625

Next, we need to find the area to the right of this z-score using a standard normal distribution table or a calculator. The probability is the complement of this area, so we subtract it from 1.

Let's say the area to the right of the z-score is 0.425. Then, the probability is 1 - 0.425 = 0.575, or 57.5%.