Question

The number of traffic accidents that occur on a particular stretch of road during a month follows a poisson distribution with a mean of 7.37.3. find the probability of observing exactly four four accidents on this stretch of road next month. round to six decimal places.

Answer 1

Let X be the number of traffic accidents that occur on a particular stretch of road during a month. X follows a Poisson distribution with a mean of μ =7.3

The probability function of X is given by

P(X=x) = $\frac{e^{-mean} (mean)^{x}}{x!}$

We have mean =7.3

P(X=x) = $\frac{e^{-7.3} (7.3)^{x}}{x!}$

Probability of observing exactly four accidents on this stretch of road next month is

P(X=4) = $\frac{e^{-7.3} (7.3)^{4}}{4!}$

= (0.0006755 * 2839.8241)/24

P(X=4) = 1.9184113/ 24

P(X=4) = 0.0799338

P(X=4) = 0.079934

Probability that there will be exactly four accidents on this stretch of road next month is 0.079934