According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What is the probability that exactly four residents were unemployed?
A) 0.0013
B) 0.0091
C) 0.0459
D) 0.1468

Question

Quizplus · Accepted Answer

This is a binomial probability problem with n=8 trials, p=0.2 probability of success (i.e. being unemployed), and we want exactly 4 successes (i.e. 4 unemployed residents). We can use the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n!/((n-k)!k!). Plugging in the values, we get: P(X=4) = (8 choose 4) * 0.2^4 * 0.8^4 = 0.0459. Therefore, the probability that exactly four residents were unemployed is 0.0459, which corresponds to choice C.

According to a Department of Labor Report, the City of Detroit