The probability that a car will have a flat tire while driving through a certain tunnel is 0.00008.Use the Poisson approximation to the binomial distribution to find the probability that among 16,000 cars passing through this tunnel,at least one will have a flat tire.
A)0.7220
B)0.6441
C)0.2780
D)1.6462
E)0.3559

Question

Quizplus · Accepted Answer

The Poisson approximation to the binomial distribution can be used with a mean (λ) equal to np, where n is the number of trials (16,000 cars) and p is the probability of success (0.00008). Thus, λ = 16,000 * 0.00008 = 1.28. The probability of at least one car having a flat tire is 1 minus the probability of no cars having a flat tire, which is calculated using the Poisson formula: P(X ≥ 1) = 1 - P(X = 0) = 1 - (e^(-λ) * λ^0 / 0!) = 1 - e^(-1.28) ≈ 0.7220.

The Probability That a Car Will Have a Flat Tire