Question

The mean number of power outages in the city is four per year find the probability that in a given year there are exactly three outages

Answer 1

Answer:

Probability that in a given year there are exactly three outages is $0.761960$

Step-by-step explanation:

If your question has an average probability of an event happening per unit (i.e. per unit of time, cycle, event) and you want to find the probability of a certain number of events happening in a period of time (or number of events), then use the Poisson Distribution

so x is the random variable that follows the Poisson distribution

Given : $\mu=4$

formula: $P(X=x)=e^{-\mu} \mu^{x} / x !$

a) To find: $P(X=3)$

$\mathrm{P}(\mathrm{X}=3)=e^{-4}\left(4^{3}\right) / 3 !=0.1954$

To find $P(X > 2)=1-P(x \leq 2)$

$\begin{aligned}&=1-[P(x=0)+P(x=1)+P(X=2)] \\&=1-(0.01832+0.07326+0.14653) \\&=0.76190\end{aligned}$