Eighty percent of the engines manufactured on an assembly line are defective. Suppose engines are randomly...

Eighty percent of the engines manufactured on an assembly line are defective. Suppose engines are randomly selected one at a time and tested. (Round your answers to three decimal places.)

(a) What is the probability that the third nondefective engine will be found on the fifth trial?

(b) What is the probability that the third nondefective engine will be found on or before the fifth trial?

Expert Solution

1)

here this follows negative binomial distribution with parameter r =3 and p=1-0.8 =0.2

a)

probability =

P(X=5)=

(_x-1C_r-1) p^r(1−p)^(x-r) =

0.031

b)

P(X<=5)=1-P(X>=6)=

1-∑_a=0² (_xC_a)p^a(1−p)^(x-a) =

0.058

orchestra answered 2 years ago

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