If tubing averages 30 defects oer 100 meter what is the prob

If tubing averages 30 defects oer 100 meter, what is the probability of finding exactly 4 defects in a randomly chosen chosen 10-meter piece of tubing?

Solution

You use poisson distribution
so if you know that the average for 100m is 30..
then for 10m it is 3 (divide by 10)
so lamda = 3
and x (=the number of defects) = 2

then you use the formula:
prob[ 4 defects in 10 meter ] = e^-lamda * (lamda^x / x !)

= e^-3 x ( 3^4 / 4!) =  0.1680314 .........i.e your option (d)...