Question

The average number of road accidents that occur on a particular stretch of road during a year is 11.

P (X = k) n
k s
Using the Poisson distribution formula, what is the probability of observing exactly 7 accidents on this stretch of road next year

Answer 1

0.06

Explanation:

Given that :

Average number of road accident (n) = 11

Probability of observing exactly 7 accident o. The stretch of road next year

Poisson random variable (k) = 7

Using the poisson distribution formula :

P(x = k) = (n^k * e^-n) / k!

P(x = 7) = (11^7 × e^-11) / 7!

P(x = 7) = (19487171 × 0.0000167017) / 5040

P(x = 7) = 325.4688838907 / 5040

P(x = 7) = 0.0645771

= 0.06