The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will
Have a flat tire. Round your answer to four decimal places.
A) 0.1217
B) 0.1947
C) 0.1460
D) 0.8783
E) 0.1703

Question

Quizplus · Accepted Answer

The Poisson distribution is given by:P(X = k) = (e^-λ * λ^k) / k!where:λ is the mean number of eventsk is the number of eventsIn this case, λ = 14,000 * 0.00005 = 0.7.So, the probability that exactly two cars will have a flat tire is:P(X = 2) = (e^-0.7 * 0.7^2) / 2! = 0.1217Therefore, the correct answer is A.

The Probability That a Car Will Have a Flat Tire