Question

Suppose a shipment of 140 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality control engineer randomly selects 4 of the components and test them. If 1 or more of the components is defective, the shipment is rejected. what is the probability that the shipment rejected?

Answer 1

140 components contain 4 defectives              
p = 4/140 = 0.0286       …Proportion of defective components      
n = 4       …sample of 4 components selected      
Let X be the number of components defective in the sample of 4 components              
Then X ~ Binomial(n = 4, p = 0.0286)              
Shipment is rejected if 1 or more component is defective              
To find P(shipment is rejected)              
that is to find P(X ≥ 1)              
P(X ≥ 1) = 1 - P(X = 0)              
We use Excel function BINOM.DIST to find the probability              
P(X ≥ 1) = 1 - BINOM.DIST(0, 4, 0.0286, FALSE)              
                = 1 - 0.8904              
                = 0.1096               
P(shipment is rejected) =