Question

College-pro painting does home interior and exterior painting. the company uses inexperienced painters that do not always do a high-quality job. it believes that its painting process can be described by a poisson distribution with an average of 4.8 defects per 400 square feet of painting. what is the probability that a 400-square-foot painted section will have fewer than 6 blemishes?

Answer 1

To solve we can use Poisson probability formula:
$P(x,\mu)=\frac{e^{-\mu}\mu^x}{x!}$
$\mu$ is the mean value of successes that happen in a given region.
x is the number of successes that are actually occurring in the given region. In our case x is 5, 4, 3, 2, 1 and 0. If a painter made 5, 4, 3, 2, 1 or no mistakes he made fewer than 6 mistakes. As these events are exclusive (you can't make 2 and 5 mistakes at the same time) we just add all those probabilities.
$\mu$ in our case is 4.8.
The final answer would be:
$(P(5)+P(4)+P(3)+P(2)+P(1)+P(0))=0.60$