Question

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.0.1947
C. 0.1460
D.0.1217

Answer 1

Answer: D. 0.1217

Explanation:

Given : The probability that a car will have a flat tire while driving through a certain tunnel :p=0.00005.

n= 14000

Then, the mean number of cars will have a flat tire while driving through a certain tunnel = np

`=14000*0.00005=0.7`

Poisson Distribution Formula :
`P(x)=(e^(-\lambda) \lambda^x)/(x!)`

For x= 2

`P(2)=(e^(-0.7) (0.7)^2)/(2!)=0.121663399429\approx0.1217`

Hence, the required probability = 0.1217