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 [tex]\mu=26[/tex] mpg and standard deviation [tex]\sigma=12[/tex] 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,
[tex]z=\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The portability is given by, [tex]P(X<28)[/tex]
[tex]=P(\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<\dfrac{28-26}{\frac{12}{\sqrt{36}}})[/tex]
[tex]=P(\dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<\dfrac{2}{\frac{12}{6}})[/tex]
[tex]=P(z<\dfrac{2}{2})[/tex]
[tex]=P(z<1)[/tex]
Using z-table,
[tex]=0.8413[/tex]
Therefore, the probability the average mpg is less than 28 mpg is 0.8413.
Answer:
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.
Step-by-step explanation:
