CollegePro Painting does home interior and exterior painting

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?

A. 0.3414

B. 0.2818

C. 0.4857

D. 0.6510

Solution

(1) Given X~Poisson(mean=4.8)

P(X=x)=(4.8^x)*exp(-4.8)/x!

So P(X<6) = P(X=0)+P(X=1)+...+P(X=5)

=(4.8^0)*exp(-4.8)/1+...+(4.8^5)*exp(-4.8)/5!

=0.6510064

Answer: d. 0.6510

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(2) P(X<=7) = P(X=0)+...+P(X=7) =0.8866662

So the probability is

0.8866662^6 =0.4859157

Answer: a. 0.4857

(2)