Answered

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.

Answer :

elcharly64

Answer:

[tex]26.5265<x<29.8735[/tex]

Step-by-step explanation:

Confidence Interval

When the population standard deviation [tex]\sigma[/tex] is known, the formula for a confidence interval for a population mean [tex]\bar x[/tex] is:

[tex]\displaystyle \bar x \pm z\frac{\sigma}{\sqrt{n}}[/tex]

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

[tex]\bar x=28.2,\ \sigma=2.7, \ n=10[/tex]

Calculating the confidence interval

[tex]\displaystyle 28.2 \pm 1.96\frac{2.7}{\sqrt{10}}[/tex]

[tex]\displaystyle 28.2 \pm 1.6735[/tex]

Or, equivalently

[tex]26.5265<x<29.8735[/tex]

Other Questions