Table 1P(X

6. (10 points) Xavier and Yvette are real estate agents. Let X denote the number of houses that Xavier will sell in a month and let Y denote the number of houses Yvette will sell in a month with the following joint probabilities of ( X, Y ) Y =OY=1 X =0 0.4 0.2 X = 0.3 0.1 (a) Find the conditional mean E(Y|X = 0) and the conditional mean E( Y| X = 1). (b) Let E(Y|X) = Bo + 31X. Find B1. Explain why 31 = E(Y|X = 1) - E(Y|X = 0). 7. (10 points) Answer the following. (a) According to the American Academy of Cosmetic Dentistry, 50% of adults believe that an unattractive smile hurts career success. Suppose that 100 adults are randomly selected. What is the probability that 60 or more of them would agree with the claim? (b) A psychologist believes that 80% of male drivers when lost continue to drive hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 100 male drivers and asked each what they did when lost. If the belief is true, determine the probability that more than 60% said they continue driving. 8. (10 points) A certain type of tomato seed germinates 80% of the time. (a) A backyard farmer planted 20 seeds. What is the probability that more than 70% germinates? (b) A backyard farmer planted 100 seeds. What is the probability that more than 70% germinates? 9. (10 points) According to the last census, 70% of working men held full-time jobs in 2010. (a) If a random sample of 20 men is drawn, what is the probability that less than 80% hold full-time jobs? (b) If a random sample of 100 men is drawn, what is the probability that less than 80% hold full-time jobs? 10. (10 points) In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow this rule. As a test, he randomly samples 100 cars driving in the rain and counts the number whose headlights are turned on. He finds this number to be 20. Does the officer have enough evidence at the 10% significance level to support his belief