Suppose the speeds of vehicles traveling on a highway are normally distributed and have a known population standard deviation of 7 miles per hour and an unknown population mean. A random sample of 32 vehicles is taken and gives a sample mean of 64 miles per hour.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level. You may use a calculator or the common z values above. Round the final answer to two decimal places.

Z0.10 Z0.05 Z0.025 Z0.01 Z0.005
1.282 1.645 1.960 2.326 2.576

The margin of error for the confidence interval for the population mean with a 98% confidence level is 2.88 miles per hour.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Find the margin of error for the confidence interval for the population mean with a 98% confidence level.

The margin of error for the confidence interval for the population mean with a 98% confidence level is 2.88 miles per hour.

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step-by-step explanation: