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

Step-by-step 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

$=14000\times0.00005=0.7$

Poisson Distribution Formula : $P(x)=\dfrac{e^{-\lambda} \lambda^x}{x!}$

For x= 2

$P(2)=\dfrac{e^{-0.7} (0.7)^2}{2!}=0.121663399429\approx0.1217$

Hence, the required probability = 0.1217