Question

On average, a painter misses 5 spots per room while painting houses. Write your answers to three decimal places.

What is the probability that in the next room he:

A) will forget to paint a maximum of 4 spots?

B) will forget no spots?

C) Find the mean of the number of unpainted spots in a house of 7 rooms.

Answer 1

A) P(X≤4) = P(X=0) +P(X=1) +P(X=2) +P(X=3) +P(X=4)

$= e^{-λ}( \frac{λ^0}{0!} + \frac{λ^1}{1!}+\frac{λ^2}{2!}+\frac{λ^3}{3!}+\frac{λ^4}{4!}) \\ = e^{-5}( 1 + 5 + 12.5+20.83+26.04 ) \\ = 0.006737 \times 65.37 \\ =0.4404$

B) $P(X=0) = \frac{e^{-5} \times 5^0}{0!} = 0.006737$

C) The mean of the number of unpainted spots in a house of 7 rooms $= 7 \times 5 = 35$