Question

A certain large shipment comes with a guarantee that it contains no more than 20% defective items. If the proportion of items in the shipment is greater than 20%, the shipment may be returned. You draw a random sample of 10 items and test each one to determine whether it is defective. Assume

	X	P(X)
P ( X = 0) = C (10,0) * 0.2^0 * ( 1 - 0.2)^10=	0	0.1074
P ( X = 1) = C (10,1) * 0.2^1 * ( 1 - 0.2)^9=	1	0.2684

p(x >=2) = 1- (p(0) +p(1))

= 1- (0.1074 + 0.2684)

= 0.6242

5.             based on the above, if 20% of the items in the shipment are defective, would 2 defectives in a sample of 10 be an unusually large number?
6.              If you found that 2 of 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.
7.             Find the variance, σ2=
8.               Find the standard deviation, σ=

Answer 1

c) variance=n*p*q= 1.6

D) SD = 1.2649