Question

Individual gas mileages (in miles per gallon) of Model Extra SS (Extra Super-Sporty) sedans are normally distributed with a population mean of 20 and a population standard deviation of 2. Based on these information, if you bought a Model Extra SS sedan, what is the probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5

Answer 1

Answer: 0.1974

Explanation:

Let X be a random variable that denotes the gas mileage (in miles per gallon) of the individual sedan.

Given: Population mean:
`\mu=20`

Standard deviation:
`\sigma=2`

The probability that the gas mileage (in miles per gallon) of your single, individual sedan is between 19.5 and 20.5:

`P(19.5<x<20.5)=P((19.5-20)/(2)<(x-\mu)/(\sigma)<(20.5-20)/(2))\\\\=P(-0.25<z<0.25)=2P(0.25)-1 [P(-z<Z<z)=2P(Z<z)-1]\\\\=2(0.5987)-1=0.1974`

The required probability=0.1974