**I don't want the answer, I want to know how to set the problem up and the formula that I need to use. I am online with a tutor right now, and they can't help me. :-(

The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and assume the population standard deviation is $.20.

1. What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean (to 4 decimals)?

Z = (score-mean)/standard error of the mean (SEm)

Scores = (mean-.03) and (mean+.03)

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z scores.

To find the probability that the mean price for a sample of 30 service stations is within $0.03 of the population mean, we need to use the concept of the sampling distribution of the sample mean.

First, let's determine the standard deviation of the sampling distribution, also known as the standard error.

The formula to calculate the standard error is:
Standard Error = Population Standard Deviation / Square Root of Sample Size

In this case, the population standard deviation is given as $0.20, and the sample size is 30. So, we can calculate the standard error as follows:

Standard Error = $0.20 / √30

Once we have the standard error, we can use it to calculate the probability using the normal distribution. Since we want to find the probability within $0.03 of the population mean, we need to calculate the probability between two values.

To do this, we convert the $0.03 into a z-score. The z-score tells us how many standard deviations away from the mean our desired value is. The formula to convert a value into a z-score is:

z = (Desired Value - Population Mean) / Standard Error

In this case, the desired value is $0.03, the population mean is $2.34, and the standard error calculated earlier is the denominator.

Once we have the z-score, we can use a standard normal distribution table or a calculator to find the corresponding probability.

Keep in mind that since we are looking for the probability within $0.03, we need to find the area between two z-scores: one for $2.37 (population mean + $0.03) and one for $2.31 (population mean - $0.03).

Using the z-scores, we can find these probabilities and subtract the cumulative probability of $2.31 from the cumulative probability of $2.37.

I hope this helps you set up the problem and find the formula you need! Don't hesitate to ask if you have any further questions.