Your firm manufactures computers You are sent a very large s

Your firm manufactures computers. You are sent a very large shipment of chips by a supplier. You want to accept this shipment only if ten percent or less of the chips are defective, which is the supplier’s claim. Your procedure for deciding whether to accept the shipment is to randomly select a sample of 10 chips, test them, and accept the shipment if there are either zero defectives or one defective among the ten.

1. If in fact ten percent of the shipment is defective, what is the probability that you will accept the shipment?

a. 0.349 c. 0.039

b 0.387 d. 0.736

2. Suppose you discover three defectives among the ten in your sample. Which is “more likely,” (i) there really are ten percent defectives, and this particular sample of ten is unusual, or (ii) the true proportion of defectives is twenty percent?

a. p = 0.10 is more likely b. p = 0.20 is more likely 2

3. Suppose instead that the shipment is small—say your company receives a shipment of twenty chips. Your procedure for deciding to accept the shipment is the same—you randomly select 10 chips, and accept the shipment if, in this sample, you find either zero or one defective. If in fact there are two defective chips in the shipment, what is the probability that you will accept the shipment?

a. 0.763 c. 0.789 b 0.5 d. 0.526

Solution

Q1.

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 < = 1) = P(X=1) + P(X=0) +   
= ( 10 1 ) * 0.1^1 * ( 1- 0.1 ) ^9 + ( 10 0 ) * 0.1^0 * ( 1- 0.1 ) ^10 +
= 0.736