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 0.00005. Use the Poisson approximation to the binomial distribution to find the probability that among 8000 cars
Passing through this tunnel, at most two will have a flat tire.
A)0.062
B)0.054
C)0.938
D)0.992

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 0.00005. Use the Poisson approximation to the binomial distribution to find the probability that among 8000 cars
Passing through this tunnel, at most two will have a flat tire. 
A)0.062
B)0.054
C)0.938
D)0.992

Quizplus · Accepted Answer

To use the Poisson approximation, first calculate the mean (λ) as the product of the number of trials (n) and the probability of success (p). Here, λ = 8000 * 0.00005 = 0.4. The probability of at most 2 cars having a flat tire is the sum of the probabilities of 0, 1, and 2 cars having a flat tire, calculated using the Poisson formula: P(X=k) = (e^(-λ) * λ^k) / k!, for k=0, 1, 2. Summing these probabilities gives a result close to 0.992.

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