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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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Two suppliers each supplied 2000 parts that were evaluated

Chapter 2, Problem 227SE

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QUESTION:

Two suppliers each supplied 2000 parts that were evaluated for conformance to specifications. One part type was more complex than the other. The proportion of nonconforming parts of each type are shown in the table.

One part is selected at random from each supplier. For each supplier, separately calculate the following probabilities:

(a) What is the probability a part conforms to specifications?

(b) What is the probability a part conforms to specifications given it is a complex assembly?

(c) What is the probability a part conforms to specifications given it is a simple component?

(d) Compare your answers for each supplier in part (a) to those in parts (b) and (c) and explain any unusual results.

Questions & Answers

QUESTION:

Two suppliers each supplied 2000 parts that were evaluated for conformance to specifications. One part type was more complex than the other. The proportion of nonconforming parts of each type are shown in the table.

One part is selected at random from each supplier. For each supplier, separately calculate the following probabilities:

(a) What is the probability a part conforms to specifications?

(b) What is the probability a part conforms to specifications given it is a complex assembly?

(c) What is the probability a part conforms to specifications given it is a simple component?

(d) Compare your answers for each supplier in part (a) to those in parts (b) and (c) and explain any unusual results.

ANSWER:

Solution:

Step 1 of 3:

Two suppliers each supplied 2000 parts that were evaluated for conformance to specifications.

The proportion of nonconforming parts of each type are given.

                       

Supplier

Simple component

Complex Assembly

Total

1

Nonconforming  

2

10

12

Total

1000

1000

2000

2

Nonconforming

4

6

10

Total

1600

400

2000

  1. We have to find the probability that a part conforms to specifications.

  1. We have to find the probability that a part conforms to specifications given it is a complex assembly.

  1. We have to find the probability that a part conforms to specifications given it is a simple component.

  1. We have to find the probability that a part conforms to specifications given it is a simple component.

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