1) According to the CDC, 7.28% of babies born in 2021 were born in February; and 9.02% of babies born in 2021 were born in August. Consider a randomly chosen baby born in 2021. a) Could this baby have been born in both February and August? b) Use your answer from a) and one of our probability rules to calculate the probability that the baby was born in February or August. c) Use your answer from b) and one of our probability rules to calculate the probability that the baby was not born in February or August. [Previous Exam Q] 2) Suppose a pregnancy test has a sensitivity of 85% and a specificity of 95%. a) If, on average, one out of every four women who take a pregnancy test is truly pregnant, what is the prevalence of pregnancy within this population of test-takers? b) Use your answer from a) and the other provided information to calculate the probability that a positive result using this test means that the woman who took it is truly pregnant. (Hint: This is the PV+) 3) If I have two random samples from the same population, the first based on 10 people and the second based on 1000 people, and I calculate the sample mean X for each of them... a) Will the expected values of those two sample means be the same? Briefly justify your answer. b) Which sample mean will have the smaller variance? Briefly justify your answer.