91Ó°ÊÓ

The undergraduate admission rate at Harvard University is about \(6 \%\) a. Assuming the admission rate is still \(6 \%\), in a sample of 100 applicants to Harvard, what is the probability that exactly 5 will be admitted? Assume that decisions to admit are independent. b. What is the probability that exactly 95 out of 100 applicants will be rejected?

A fair die is rolled 60 times. a. What is the expected number of times that an odd number will turn up? b. Find the standard deviation for the outcome to be an odd number. c. How many times should you expect odd numbers to turn up, give or take how many times? Based on these numbers, give the range of the number of times odd numbers can turn up.

A study of human body temperatures using healthy men showed a mean of \(98.1^{\circ} \mathrm{F}\) and a standard deviation of \(0.70^{\circ} \mathrm{F}\). Assume the temperatures are approximately Normally distributed. a. Find the percentage of healthy men with temperatures below \(98.6^{\circ} \mathrm{F}\) (that temperature was considered typical for many decades). b. What temperature does a healthy man have if his temperature is at the 76 th percentile?

The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100 , and the scores are approximately Normally distributed. a. What is the probability that one randomly selected person will have an SAT score of 550 or more? b. What is the probability that four randomly selected people will all have SAT scores of 550 or more? c. For 800 randomly selected people, what is the probability that 250 or more will have scores of 550 or more? d. For 800 randomly selected people, on average how many should have scores of 550 or more? Round to the nearest whole number. e. Find the standard deviation for part d. Round to the nearest whole number. f. Report the range of people out of 800 who should have scores of 550 or more from two standard deviations below the mean to two standard deviations above the mean. Use your rounded answers to part \(\mathrm{d}\) and \(\mathrm{e}\). g. If 400 out of 800 randomly selected people had scores of 550 or more, would you be surprised? Explain.