Suppose the number of business majors at liberal arts colleges are normally distributed and have a known population standard deviation of 21 students and an unknown population mean. A random sample of 35 liberal arts colleges is taken and gives a sample mean of 420 business majors. Find the margin of errorfor the confidence interval for the population mean with a 90% confidence level. Round the final answer to two decimal places.

The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.

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.

In this question:

So

The margin of error for the confidence interval for the population mean with a 90% confidence level is of 5.84 business majors.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.