Question

Twelve jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 47% are of a minority race. Of the 12 jurors selected, 2 are minorities.

(a) What proportion of the jury described is from a minority race?
(b) If 12 jurors are randomly selected from a population where 47% are minorities, what is the probability that 2 or fewer jurors will be minorities?
(c) What might the lawyer of a defendant from this minority race argue?
(a) The proportion of the jury described that is from a minority race is
(Round to two decimal places as needed.)
(b) The probability that 2 or fewer out of 12 jurors are minorities, assuming that the proportion of the population that are minorities is 47%, is
(Round to four decimal places as needed.)
(c) Choose the correct answer below.
OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.
B. The number of minorities on the jury is reasonable, given the composition of the population from which it came.
OC. The number of minorities on the jury is unusually high, given the composition of the population from which it came.
OD. The number of minorities on the jury is impossible, given the composition of the population from which it came.
Next

Answer 1

Explanation:

(a) Proportion of minority jurors = 2/12 = 1/6 = 0.1667

(b) Using binomial distribution, P(2 or fewer minorities) = P(0 minorities) + P(1 minority) + P(2 minorities)

P(0 minorities) = (0.53)^12 ≈ 0.005

P(1 minority) = 12C1 (0.47)(0.53)^11 ≈ 0.048

P(2 minorities) = 12C2 (0.47)^2(0.53)^10 ≈ 0.18

P(2 or fewer minorities) ≈ 0.005 + 0.048 + 0.18 ≈ 0.2339

(c) OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.