Question

For a manufacturing industry, the number of industrial accidents averages three per week.

a.    Find the probability that at most five accidents will occur in a given week. 

b.    Find the probability that two accidents will occur in a given day.

Answer 1

$x=number\:of\:accidents\:per\:week\:$

$Average\:number\:per\:week\left(\lambda \right)=3$

The\:poisson\:distribution\:function=\frac{e^{-\lambda }\lambda \:^x}{x!}\:\:\:x=1,2,3....

a. $P\left(x\le 5\right)=P\left(x=0\right)+P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)+P\left(x=4\right)+P\left(x=5\right)$

$=0.8173$

b. The average number of accidents per day is given as:

$\:\lambda _d=\frac{3}{7}$

$y=number\:of\:accidents\:per\:given\:day$

$P\left(y=2\right)=\frac{e^{-\frac{3}{7}}\left(\frac{3}{7}\right)^2}{2!}=0.00001312$