Question

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48:11
the average miles per gallon of a particular automobile model are approximately normally distributed with a given mean $mu = 43.8$ miles per gallon and standard deviation $sigma = 5.1$ miles per gallon. what percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?
$\bigcirc$ 68%
$\bigcirc$ 75%
$\bigcirc$ 95%
$\bigcirc$ 100%

Explanation:

Step1: Calculate z-score for 38.7

The z-score formula is $z = \frac{x - \mu}{\sigma}$.
$z_1 = \frac{38.7 - 43.8}{5.1} = \frac{-5.1}{5.1} = -1$

Step2: Calculate z-score for 48.9

Use the same z-score formula.
$z_2 = \frac{48.9 - 43.8}{5.1} = \frac{5.1}{5.1} = 1$

Step3: Apply empirical rule

For a normal distribution, ~68% of data lies within $z=-1$ and $z=1$.

Answer:

68%