Question

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? 68% 75% 95% 100%.

Answer 1

The percentage of automobiles has average miles per gallon between 38. 7 miles per gallon and 48. 9 miles per gallon is 68%.

What is Percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

We know that the standard deviation of the automobiles is 5.1 miles per gallon, while the mean of the automobiles is 43.8 miles per gallon.

Now, since we need to find the value of the percentage of the automobiles that have average miles per gallon between 38. 7 miles per gallon and 48. 9 miles per gallon, therefore, we can write the probability as,

$P(\dfrac{38.7-43.8}{5.1}\leq Z \leq \dfrac{48.9-43.8}{5.1})\\\\=P(-1 \leq Z\leq 1)\\\\= P(Z\leq 1) - P(Z\leq -1)$

Now, check the z table to find the values of -1 and 1,

$= P(Z\leq 1) - P(Z\leq -1)\\\\= 0.8413 - 0.1587\\\\= 0.6826\\\\= 68.26\% \approx68\%$

Hence, the percentage of automobiles has average miles per gallon between 38. 7 miles per gallon and 48. 9 miles per gallon is 68%.

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