In determining automobile mileage ratings,
it was found that the mpg in the city for a certain...

Question

In determining automobile mileage ratings,
it was found that the mpg in the city for a certain model is normally
distributed, with a mean of 30 mpg and a standard deviation of 1.0 mpg. Suppose
that the car manufacturer samples 5 cars from its assembly line and tests them
for mileage ratings. 

a. What is the distribution of the mean mpg
for the sample? 

b. What is the probability that the sample
mean will be greater than 31 mpg? 

c. What is the probability that the sample
mean will be less than 29.5 mpg?

Atreye · Accepted Answer

Solution a:
Let  be the mean mpg for the sample and  be the standard deviation and n is the sample size.
The distribution of the mean mpg for the sample is that is .
Solution b:
The probability that the sample mean will be greater than 31 mpg is calculated as below:
Solution c:

In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.0 mpg. Suppose that...

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