Of the parts produced by a particular machine 08 are defecti

Of the parts produced by a particular machine, 0.8% are defective. If a random sample of 12 parts produced by this machine contains 2 or more defective parts, the machine is shut down for repairs. Find the probability that the machine will be shut down for repairs based on this sampling plan. (Give your answer correct to five decimal places.)

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 2) = P(X=1) + P(X=0) +
= ( 12 1 ) * 0.008^1 * ( 1- 0.008 ) ^11 + ( 12 0 ) * 0.008^0 * ( 1- 0.008 ) ^12 +   
= 0.996

P( X > = 2 ) = 1 - P( X < 2) = 0.004