A random sample of n measurements was selected from a population with unknown mean and standard deviation =30 for each of the situations in parts a through d. Calculate a 90% confidence interval for for each of these situations.

a. n=75, x=26

b. n=150, x=106

c. n=120, x=15

d. n=120, x=4.99

e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a throughd? Explain.

A random sample of 87 observations produced a mean x=25.5 and a standard deviation s=2.8.

a. Find a95% confidence interval for .

b. Find a90% confidence interval for .

c. Find a99% confidence interval for .