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

Answer:

The 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 $\mu=26$ 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,

$z=\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

The portability is given by, $P(X$

$=P(\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=P(\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=P(z$

$=P(z$

Using z-table,

$=0.8413$

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