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)0.6174
B)0.3826
C)0.8131
D)0.1869

Question

Quizplus · Accepted Answer

This is a binomial probability problem. Let X be the number of cars with both headlights working out of a sample of 8 cars. Then X has a binomial distribution with n=8 and p=0.9. We want to find P(X≥7). We can use the binomial formula or a binomial probability table. Using the binomial formula, we have:

P(X≥7) = P(X=7)+P(X=8) = (8 choose 7) (0.9)^7 (0.1)^1 + (8 choose 8) (0.9)^8 (0.1)^0
          = 8(0.9)^7 (0.1) + (0.9)^8 
          = 0.9890

Using a binomial probability table, we look up P(X≥7) for n=8 and p=0.9, which gives us 0.9890. Therefore, the answer is C.

If 90 Percent of Automobiles in Orange County Have Both