2. A random sample of n564 observations has a mean x 529.1 and a standard deviation s53.9.

a. Give the point estimate of the population mean m and find the margin of error for your estimate.

b. Find a 90% confidence interval for m. What does

“90% confident” mean?

c. Find a 90% lower confidence bound for the population mean m. Why is this bound different from the lower confidence limit in part b?

d. How many observations do you need to estimate m to within .5, with probability equal to .95?