GMAT Scores:

Total scores on the GMAT are normally distributed and historically have a population standard deviation of 113.The Graduate Management Admission Council (GMAC), who administers the test, claims that the mean total score is 529. Suppose a random sample of 8 students took the test, and their scores are given below: (hint: assume s = 113)

699, 560, 414, 570, 521, 663, 727, 416

PLEASE TYPE ANSWER FOR LEGIBILITY. ANSWER ALL QUESTIONS OR LEAVE IT FOR SOMEONE WHO WILL.

a)Find a point estimate for the population mean

b)Construct a 95% confidence interval for the true mean score for the population.

c)Does this interval contain the value reported by GMAC?

d)How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?

e)How many students should be surveyed to estimate the mean score within 25 points with 95% confidence?

f)How many students should be surveyed to estimate the mean score within 25 points with 99% confidence?