The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 16. A random sample of 420 salespeople was taken and the mean number of cars sold annually was found to be 69. Find the 91% confidence interval estimate of the population mean.

Following are the calculation to the Confidence Interval:

Given:

To find:

Confidence Interval=?

Solution:

Here,

Therefore,

Now, confidence interval:  

Therefore, the final answer is "".

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The 91% confidence interval estimate of the population mean is between 67.68 and 70.32 cars sold annually.

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.

The lower end of the interval is the sample mean subtracted by M. So it is 69 - 1.32 = 67.68.

The upper end of the interval is the sample mean added to M. So it is 69 + 1.32 = 70.32

The 91% confidence interval estimate of the population mean is between 67.68 and 70.32 cars sold annually.