Final answer:
Using the normal distribution, a Z-score calculation for 24 mpg results in finding that approximately 84% of the vehicles have a gas mileage greater than 24 mpg.
Step-by-step explanation:
To determine the percentage of vehicles that have a gas mileage greater than 24 mpg, we can use the properties of the normal distribution. Given the average (mean) gas mileage is 26 mpg with a standard deviation of 2 mpg, we can calculate the Z-score for a gas mileage of 24 mpg.
The Z-score is given by the formula:
Z = (X - μ) / σ
Where X is the value we are interested in (24 mpg), μ is the mean (26 mpg), and σ is the standard deviation (2 mpg).
Z = (24 - 26) / 2 = -2 / 2 = -1
A Z-score of -1 corresponds to a percentile rank of approximately 15.87% on the lower end, meaning 15.87% of vehicles have a gas mileage less than 24 mpg. To find the percentage greater than 24 mpg, we subtract this from 100%.
100% - 15.87% = 84.13%
Therefore, approximately 84% of the vehicles produced by the company have a gas mileage greater than 24 mpg.