Page 167, 3.1.30.* Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate about 5% defective items. Let X be the number of defective items in a sample without replacement of size n = 10. Suppose the factory returns the shipment if X ≥ 1. (a) Obtain the probability that the factory returns a shipment of items that has 5% defective items. (b) Suppose the shipment has 10% defective items. Obtain the probability that the factory returns such a shipment. (c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial distributions.
Page 167, 3.1.30.* Consider a shipment of 1000 items into a factory. Suppose the factory can tolerate about 5% defective items. Let X be the number of defective items in a sample without replacement of size n = 10. Suppose the factory returns the shipment if X ≥ 1. (a) Obtain the probability that the factory returns a shipment of items that has 5% defective items. (b) Suppose the shipment has 10% defective items. Obtain the probability that the factory returns such a shipment. (c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial distributions.
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Transcribed Image Text:Page 167, 3.1.30.* Consider a shipment of 1000 items into a factory. Suppose the factory can
tolerate about 5% defective items. Let X be the number of defective items in a sample without
replacement of size n = 10. Suppose the factory returns the shipment if X > 1.
(a) Obtain the probability that the factory returns a shipment of items that has 5% defective
items.
(b) Suppose the shipment has 10% defective items. Obtain the probability that the factory
returns such a shipment.
(c) Obtain approximations to the probabilities in parts (a) and (b) using appropriate binomial
distributions.
Expert Solution
Step 1
N= 1000
Tolerance= 5%
Size(n)=10
Factory returns the shipment if X≥1
* Here two both ( N and n ) is given so clearly it is hypergeometric distribution.
For 5% :
D= N*5% = 1000*5/100 = 50
For 10%
D= 1000*10/100 = 100
Formula for hypergeometric probability :
P(x) = (N-DCn-x)*(DCx)/(NCn)
Formula for combination :
NCr= n!/[(N-r)!*r!]
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