Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 45 miles and a standard deviation of 8 miles. Find the probability of the following events: A. The car travels more than 53 miles per gallon. Probability

Answer 1

15.87% probability that the car travels more than 53 miles per gallon.

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 45, \sigma = 8`

Find the probability of the following events: A. The car travels more than 53 miles per gallon. Probability

This is the pvalue of Z when X = 53. So

`Z = (X - \mu)/(\sigma)`

`Z = (53 - 45)/(8)`

`Z = 1`

`Z = 1` has a pvalue of 0.8413

1 - 0.8413 = 0.1587

15.87% probability that the car travels more than 53 miles per gallon.