1. Suppose that 8% of a population is infected with a virus. There are no obvious symptoms that can be used to recognize carriers, thus individuals must be selected at random and tested. We can assume the test to detect infected individuals is 100% accurate. If a sample of l 0 individuals from the population are tested, what is the probability that at most one ofthem is infected? (210:) One researcher=s goal is to find at least one person who is infected with the virus for observation. Ifshe samples too few people= there is a risk ofnot nding any carriers, while testing too many people will waste valuable testing resources. What is the minimum sample size she needs in order to detect at least one infected individual with a probability of at least 90%? Justify your answer. (2p?) 2. We want to compare the grades on an introductory biology exam (100 points total) for freshman versus sophomores. Suppose that 68% percent of the class are freshman, while the remaining are sophomores. The exam grades for freshman were normally distributed, with a mean of 84 and a standard deviation of 15. The exam grades for sophomores were also normally distributed, and 40% of the entire class got an \"A' on the test (scored at least 90). a. Students who did better than 80% of the freshman in the class got at least what grade? (2P1) What proportion of freshman got a \"B\" on the test (scored between 30 and 90)? (33'?) What proportion of sophomores got an \"A on the test? (3p!) If the standard deviation of exam grades for sophomores is the same as it is for freshman, what is the mean sophomore grade on the exam? (31m?)