Develop 90 %, 95 %, and 99% confidence intervals for population mean (µ) when sample mean is 10 with the sample size of 100

1)
a. Develop 90 %, 95 %, and 99% confidence intervals for population mean (µ) when sample mean is 10 with the sample size of 100. Population standard deviation is known to be 5.
b. Suppose that sample size changes to 144 and 225. Develop three confidence intervals again. What happens to the margin of error when sample size increases?
c. A simple random sample of 400 individuals provides 100 yes responses. Compute the 90%, 95%, and 99% confidence interval for population proportion (p).
d. With the same random sample as in 3, if the sample size increases to 1000, what happens to the three confidence intervals?

2)
Suppose you would like to conduct a survey to determine the yearly consumption of beef by a typical American and want to use 3 pounds as the desired margin of error estimate of the population mean amount of beef consumed annually. Use 25 pounds as the population standard deviation and recommend a sample size for each of the following situations:
a. A 90% confidence interval is desired.
b. A 95 % confidence interval is desired.
c. A 99% confidence interval is desired.
d. When the desired margin of error is set, what happens to the sample size as the confidence level is increased? Would you recommend using 99% confidence interval in this case? Expla