A political committee consists of six Democrats and eight Republicans. A subcomm

Question

A political committee consists of six Democrats and eight Republicans. A subcommittee of seven people needs to be formed from this group. (For this problem define a success as a Democrat being selected for the subcommittee.) Determine the probability that this subcommittee will consist of three Democrats and four Republicans if they were randomly selected. Calculate the mean and standard deviation of this distribution. The probability that this subcommittee will consist of three Democrats and four Republicans if they were randomly selected is. (Round to four decimal places as needed.)

Explanation / Answer

total = 6 + 8 = 14

P(democrats), p = 6 / 14 =0.43

n = 7

a) P(3 democrats) = 7C3 * 0.433 * (1 - 0.43)7-3

                              = 0.2937

b) mean = n * p = 7 * 0.43 = 3.01

standard deviation = sqrt(n * p * (1-p)) = sqrt(7 * 0.43 * (1-0.43)) = 1.31

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