Please help me better understand with detailed explanations and excel functions and graphs if applicable. Thank you!

Problem-6

The mean annual cost of automobile insurance is $939. Assume that the standard deviation is $245.

a) What is the probability that a simple random sample of automobile insurance policies will have a sample mean within $25 of the population mean for each of the following sample sizes: 30, 50, 100, and 400?

b) What is the advantage of a larger sample size when attempting to estimate the population mean?

Problem-7

A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation of the drinks dispensed of 20 milliliters. A random sample of 30 drinks from the machine had an average volume of 373 milliliters. Determine a 95% confidence interval for the average amount of all drinks dispensed by this machine.

Problem-8

A Human Resources Manager is interested in finding the average compensation for financial analysts. Through market research she obtained compensation information for a sample of 57 financial planners Summary statistics for the sample data is as follows: mean = $52,746 and standard deviation = $9,528. Calculate a 95% confidence interval for the mean compensation for the population of financial analysts under study

Problem-9

A random sample of 200 consoles were examined for a scratch defect. Of the 200 samples, 22 were found to have the defect. Find a 95% confidence interval for the population proportion of consoles with this scratch defect.