When circuit boards used in the manufacture of compact disc

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage defective rate is 10%. Let X = the number of defective boards in a random sample of size n =10. Determine P (X LE 2) Determine P (2 LE X LE 4) What is the probability that none of the 10 boards is defective? What are the mean and variance of X?

Solution

p = 0.10

X = no of defective board

x is binomial with (10, 0.10)

a) P(X<=2) = 0.6769

b) P(2<=x<=4) =0.9568 -0.3917

= 0.5651

c) P(X=0) = 0.1216

d) Mean = np = 1 and var = npq = 0.9