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miss Akunina [59]
3 years ago
15

An environmental group at a local college is conducting independent tests to determine the distance a particular make of automob

ile 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.
Mathematics
1 answer:
melomori [17]3 years ago
6 0

Answer:

26.5265

Step-by-step explanation:

<u>Confidence Interval</u>

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

\displaystyle \bar x \pm z\frac{\sigma}{\sqrt{n}}

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

\bar x=28.2,\ \sigma=2.7, \ n=10

Calculating the confidence interval

\displaystyle 28.2 \pm 1.96\frac{2.7}{\sqrt{10}}

\displaystyle 28.2 \pm 1.6735

Or, equivalently

26.5265

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