The average price per gallon of unleaded regular gasoline wa

The average price per gallon of unleaded regular gasoline was reported to be $2.34 in
northern Kentucky. Use this price as the population mean, and assume that the population
standard deviation is $0.20.
1. For a random sample of 64 service stations, find the standard deviation of the sampling
distribution of the sample mean.
2. What is the probability that the mean price for a sample of 64 service stations is within $0.03
of the population mean?

3. For a random sample of 100 service stations, find the standard deviation of the sampling

distribution of the sample mean.
4. What is the probability that the mean price for a sample of 100 service stations is within
$0.03 of the population mean?

Solution

1.

standard deviation of the sampling distribution of the sample mean.= population std deviation/sqrt(n) = 0.2/sqrt(64) = 0.2/8 = 0.025

2.

t-statistics =0.03/0.025 = 1.2

Probability = P( -1.2 < z < 1.2) = 0.7698

3.

standard deviation of the sampling distribution of the sample mean.= population std deviation/sqrt(n) = 0.2/sqrt(100) = 0.2/10 = 0.02

4.

t-statistics =0.03/0.02 = 1.5

Probability = P( -1.5 < z < 1.5) = 0.8663