In a certain community, 45% of the population is Jewish. A study shows that of 12 social service agencies, 4 have board presidents who are Jewish. Find the probability that this could happen by chance. Round your answer to six decimal places.
A) Pr(4 Jewish Presidents) = 0.169964
B) Pr(4 Jewish Presidents) = 0.076165
C) Pr(4 Jewish Presidents) = 0.041006
D) Pr(4 Jewish Presidents) = 0.150000
E) Pr(4 Jewish Presidents) = 0.007407

Question

In a certain community, 45% of the population is Jewish. A study shows that of 12 social service agencies, 4 have board presidents who are Jewish. Find the probability that this could happen by chance. Round your answer to six decimal places. ​
A) Pr(4 Jewish Presidents) = 0.169964
B) Pr(4 Jewish Presidents) = 0.076165
C) Pr(4 Jewish Presidents) = 0.041006
D) Pr(4 Jewish Presidents) = 0.150000
E) Pr(4 Jewish Presidents) = 0.007407

Quizplus · Accepted Answer

This probability can be calculated using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials (12 agencies), k is the number of successes (4 Jewish presidents), and p is the probability of success on a single trial (0.45, since 45% of the population is Jewish). Plugging these values into the formula gives Pr(4 Jewish Presidents) = 0.169964.

In a Certain Community, 45% of the Population Is Jewish