Suppose the finishing times for cyclists in a race are normally distributed and have a known population standard deviation of 9 minutes and an unknown population mean. A random sample of 18 cyclists is talken and gives a sample mean of 146 minutes. Find the confidence interval for the population mean with a 99% confidence level. 0.10 0.05 0.025 0.005 0.01
1.282 1.645 1.960 2.326 2.576

The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes

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 146 - 5.46 = 140.54 minutes

The upper end of the interval is the sample mean added to M. So it is 146 + 5.46 = 151.46 minutes

The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes

0.038

step-by-step explanation: