Use the Poisson model to approximate the probability. Round your answer to four decimal places.
-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.
A) 0.8783
B) 0.1703
C) 0.1217
D) 0.1947
E) 0.1460

Question

Quizplus · Accepted Answer

The formula for the Poisson distribution is: 
P(X = k) = (e^-λ * λ^k) / k! 
where λ is the expected number of occurrences in the given time or space interval.

In this case, λ = (0.00005) * (14000) = 0.7

So, the probability of getting exactly two flat tires among 14,000 cars passing through the tunnel is: 
P(X = 2) = (e^-0.7 * 0.7^2) / 2! 
= 0.1217

Rounding to four decimal places gives 0.1217, which corresponds to choice C.

Use the Poisson Model to Approximate the Probability