The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005.Use the Poisson approximation to the binomial distribution to find the probability that among 14,000 cars passing through this tunnel,exactly two will have a flat tire.
A)0.8783
B)0.1217
C)0.1460
D)0.1703
E)0.1947

Question

Quizplus · Accepted Answer

The Poisson approximation is used when n is large and p is small. Here, λ = np = 14,000 * 0.00005 = 0.7. The probability of exactly k events (k=2) is given by P(X=k) = (e^(-λ) * λ^k) / k!. Substituting the values, we get P(X=2) = (e^(-0.7) * 0.7^2) / 2! = 0.1217.

The Probability That a Car Will Have a Flat Tire