If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?
A).6174
B).3826
C).8131
D).1869

Question

Quizplus · Accepted Answer

This is a binomial distribution problem, where n=8, p=0.9, and we want to find the probability of at least 7 successes. We can use the binomial probability formula or a binomial probability table to find the answer.

Using the formula: P(X≥7) = P(X=7) + P(X=8)
P(X=k) = n!/k!(n-k)! (p^k) (1-p)^(n-k)
P(X=7) = 8!/7!1!(0.9^7)(0.1^1) = 0.201326592
P(X=8) = 8!/8!0!(0.9^8)(0.1^0) = 0.43046721
P(X≥7) = 0.201326592 + 0.43046721 = 0.631793802

Therefore, the probability that in a sample of eight automobiles, at least seven will have both headlights working is 0.631793802 or approximately 0.8131 when rounded to four decimal places. Choice C is the best answer.

If 90 Percent of Automobiles in Orange County Have Both