An environmental group at a local college is conducting independent tests to determine the distance a particular make of automobile will travel while consuming only 1 gallon of gas. They test a sample of five cars and obtain a mean of 28.2 miles. Assuming that the standard deviation is 2.7 miles, find the 95 percent confidence interval for the mean distance traveled by all such cars using 1 gallon of gas.

Step-by-step explanation:

Confidence Interval

When the population standard deviation is known, the formula for a confidence interval for a population mean is:

Where n is the sample size and z is the corresponding z-value from the standard normal distribution for the selected confidence level. The value of z for a 95% confidence interval is z=1.96. The rest of the values are

Calculating the confidence interval

Or, equivalently