For the second page, i just need b., c., and d.. Ignore questions 8 and 9. 6. Re

Question

For the second page, i just need b., c., and d.. Ignore questions 8 and 9.

6. Real estate ads suggest that 65% of homes for sale have garages, 20% have swimming pools, and 15% have both features. What is the probability that a home for sale has a. a pool or a garage? b. neither a pool nor a garage? Pr(PUG) c. a pool and no garage? Pr(PA No G) = d. a garage and no pool? e. only a pool or only a garage (not both)? f. Create a Venn diagram of this scenario. Be sure to include probabilities. g. Compute the probability that a house has a garage given that it has a pool h. Compute the probability that a house has a pool given that it has a garage. Pr(P |G) 7. Suppose 30% of the population has a genetic marker of interest to a pharmaceutical company a. If the company takes a sample of 30 random people from this population, could they use the Central Limit Theorem to make predictions about the sample distribution of the population proportion? Yes No Why? 4 of 5

Explanation / Answer

6) P(P or g) = 0.65 + 0.2 - 0.15 = 0.7

P(no P or no g) = 1 - P(P and g) = 1 - 0.15 = 0.85

P(P and no g) = P(P) - P(P and g)

= 0.2 - 0.15 = 0.05

P(g and no P) = P(g) - P(g and P) = 0.65 - 0.15 = 0.5

P((P and no g) or (g and no P))= 0.05 + 0.5 = 0.55

P(g|P)= P(g and P)/P(P) = 0.15/0.2 = 0.75

P(P|G) = P(P and G)/P(G) = 0.15/0.65 = 0.23

7)a) yes because the sample size is large.

B) estimated proportion = 0.3

C) standard deviation = sqrt (p (1 - p)/n)

= sqrt(0.3 * 0.7 /30) = 0.08

D) n = 4 * 30 = 120

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