Question

PLEASE SHOW ALL WORK

Examples (2) In a painting shop, on average, there are 5 defects on the body of a painted car. Calculate a) the probability of finding a painted body with 10 defects. b) the probability of finding 10 defects on 2 painted bodies.

Answer 1

Let X denotes the number of defects on the body of a randomly selected painted car.

X ~ Poisson(5)

The probability mass function of X is

$P(X=x) = \frac{e^{-5}*5^x}{x!},x=0,1,2,3,...$

a) The probability of finding a painted body with 10 defects

$=P(X=10) = \frac{e^{-5}*5^{10}}{10!} = 0.0181328$

b)

Let Y denotes the number of defects on the body of 2 randomly selected painted car.

Y ~ Poisson(5 + 5) or Y ~ Poisson(10)

The probability mass function of Y is

$P(Y=y) = \frac{e^{-10}*10^y}{y!},y=0,1,2,3,...$

The probability of finding 10 defects on 2 painted bodies

$=P(Y=10) = \frac{e^{-10}*10^{10}}{10!}= 0.125110$