Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places.
-The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson approximation to the binomial distribution to find the probability that among 16,000
Cars passing through this tunnel, exactly two will have a flat tire.
A)0.151
B)0.173
C)0.108
D)0.130

Question

Determine the required probability by using the Poisson approximation to the binomial distribution. Round to threedecimal places.
-The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson approximation to the binomial distribution to find the probability that among 16,000
Cars passing through this tunnel, exactly two will have a flat tire. 
A)0.151
B)0.173
C)0.108
D)0.130

Quizplus · Accepted Answer

The Poisson approximation is used when n is large and p is small. Here, λ = np = 16000 * 0.00004 = 0.64. The probability of exactly k events in a Poisson distribution is given by (e^(-λ) * λ^k) / k!. For k = 2, this is (e^(-0.64) * 0.64^2) / 2! = 0.108.

Determine the Required Probability by Using the Poisson Approximation to the Binomial