Question

13) Items under inspection are subjected to two types of defects about 70% of the items in a large lot are judged to be defect-free, whereas 20% have a type A defect alone and 10% have a type B defect alone (none have both types of defects). a) If six of items are randomly selected, find the probability that three have no defects, one has type A defect, and two have type B defect. b) What is the mean and standard deviation of type A defect.

Answer 1

a) P(A) = 0.2, P(B) = 0.1, P(none) = 0.7

P(3 no defects, 1 A, and 2 B) =

$\tiny \binom{6}{3}*0.7^3 *\binom{3}{2}*0.1^2 *\binom{1}{1}*0.2 = 0.08232$

Hence, probability of 3 no defevts, one type A and two type B defects is 0.08232

b) n = 6, p = 0.2, q = 1 - 0.2 = 0.8

Var(x) = n*p*q = 6*0.2*0.8 = 0.96

I hope these will help. Thank you.