Use Bernoulli Binomial Geometric or Poisson distribution 8 l

Use Bernoulli, Binomial, Geometric or Poisson distribution

(8) ldentical computer components are shipped in boxes of 5. About 15% of components have defects. Boxes are tested in a random order. a) What is the probability that a randomly selected box has only non-defective components? b) What is the probability that at least 8 of randomly selected 10 boxes have only non-defective components? c) What is the distribution of the number of boxes tested until a box without defective components is found?

Solution

a) In a given box, let X be the number of non-defective components.

15% are Defective .So non Defective 85%
This X is Binomial,
n = 5, p = 0.85. The probability of a box with five non-defective components is
P(X = 5) = (0.85)5 = 0.44 .

b) Now, let Y be the number of boxes with only non-defective components. This Y is also
Binomial. Its parameters are n = 10 and p = 0.44, where p is calculated in (a).

P(Y>=8)=P(8)+P(9)+P(10)= 0.0249

c) c) This is precisely the number of trials needed to get the firstsuccess. Therefore, the distribution
is Geometric with p = 0.44.