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The number of defective components produced by a certain process in one day has a Poisson
distribution with mean of 20. Each defective component has probability of 0.60 of being
repairable.

(a) Find the probability that exactly 15 defective components are produced.
(b) Given that exactly 15 defective components are produced, find the probability that
exactly 10 of them are repairable.
(c) Let N be the number of defective components produced, and let X be the number of
them that are repairable. Given the value of N, what is the distribution of X?
(d) Find the probability that exactly 15 defective components are produced, with exactly 10
of them being repairable.

Respuesta :

Answer:

Step-by-step explanation:

Let X be the no of defective components produced by a certain process in one day

X is Poisson with parameter = 20

Y = no of components that can be repaired

Since each component to be repaired is independent of the other Y is Binomial with p =0.60

a) [tex]P(x=15) = 0.051649[/tex]

b) P(Y = 10)= Binomial prob (15,0.6) for y =10

= [tex]0.1859[/tex]

Here no of repairables X is binomial.

c) Prob for 15 produced and 10 repairable = product of a and b

= 0.009603

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