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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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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please answer only page 167 3.1.30

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.
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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