Question

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is approximately normal with mean 26 mpg and standard deviation 12 mpg. If a random sample of 36 such cars are chosen and tested, what is the probability the average mpg is less than 28 mpg?

Answer 1

he probability the average mpg is less than 28 mpg is 0.8413.

Step-by-step explanation:

Given : The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is approximately normal with

Mean mpg and standard deviation mpg.

Number of sample n=36

To find : What is the probability the average mpg is less than 28 mpg?

Solution :

Applying z-score formula,

The portability is given by,

Using z-table,

Therefore, the probability the average mpg is less than 28 mpg is 0.8413.

Explanation:

Answer 2

The probability the average mpg is less than 28 mpg is 0.8413.

Explanation:

Given : The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is approximately normal with

Mean
`\mu=26` mpg and standard deviation
`\sigma=12` mpg.

Number of sample n=36

To find : What is the probability the average mpg is less than 28 mpg?

Solution :

Applying z-score formula,

`z=(x-\mu)/((\sigma)/(√(n)))`

The portability is given by,
`P(X<28)`

`=P((x-\mu)/((\sigma)/(√(n)))<(28-26)/((12)/(√(36))))`

`=P((x-\mu)/((\sigma)/(√(n)))<(2)/((12)/(6)))`

`=P(z<(2)/(2))`

`=P(z<1)`

Using z-table,

`=0.8413`

Therefore, the probability the average mpg is less than 28 mpg is 0.8413.