Question

suppose that car gas efficiency in florida is normally distributed with a mean of 28.8 miles per gallon and a standard deviation of 6.2 miles per gallon. the worst 25% of florida car efficiency is

a. less than or equal to 24.62 miles per gallon
b. less than or equal to 20.6 miles per gallon
c. greater than or equal to 32.98 miles per gallon
d. greater than equal to 25 miles per gallon

Explanation:

Step1: Find the z - score

We want to find the value corresponding to the lower 25% of the normal distribution. Looking up in the standard normal distribution table (z - table), the z - score corresponding to a left - tail area of 0.25 is approximately $z=- 0.6745$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 28.8$, $\sigma=6.2$ and $z=-0.6745$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate $x$

Substitute the values into the formula: $x = 28.8+( - 0.6745)\times6.2=28.8-4.1819 = 24.6181\approx24.62$.

Answer:

A. less than or equal to 24.62 miles per gallon