Concept explainers
Determine the
Find the probability of accepting lots that are 10%, 20%, 30%, and 40% defective.
Answer to Problem 15E
The probability of accepting lots that are 10%, 20%, 30%, and 40% defective is,
Defective Percent | Probability of accepting lot |
10 | 0.889 |
20 | 0.558 |
30 | 0.253 |
40 | 0.083 |
Explanation of Solution
Calculation:
Let x denotes the accepting lots.
For 10% defective:
The probability of accepting lots that is 10% defective is,
Compute the probability values for each x using binomial probability distribution table.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.10 in probability row.
- Locate the value 0 in x column.
- The intersecting value that corresponds to 0 with probability 0.10 is 0.282.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.10 in probability row.
- Locate the value 1 in x column.
- The intersecting value that corresponds to 1 with probability 0.10 is 0.377.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.10 in probability row.
- Locate the value 2 in x column.
- The intersecting value that corresponds to 2 with probability 0.10 is 0.230.
The required probability is,
Hence, the probability of accepting lots that is 10% defective is 0.889.
For 20% defective:
The probability of accepting lots that is 20% defective is,
Compute the probability values for each x using binomial probability distribution table.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.20 in probability row.
- Locate the value 0 in x column.
- The intersecting value that corresponds to 0 with probability 0.20 is 0.069.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.20 in probability row.
- Locate the value 1 in x column.
- The intersecting value that corresponds to 1 with probability 0.20 is 0.206.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.20 in probability row.
- Locate the value 2 in x column.
- The intersecting value that corresponds to 2 with probability 0.20 is 0.283.
The required probability is,
Hence, the probability of accepting lots that is 20% defective is 0.558.
For 30% defective:
The probability of accepting lots that is 30% defective is,
Compute the probability values for each x using binomial probability distribution table.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.30 in probability row.
- Locate the value 0 in x column.
- The intersecting value that corresponds to 0 with probability 0.30 is 0.014.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.30 in probability row.
- Locate the value 1 in x column.
- The intersecting value that corresponds to 1 with probability 0.30 is 0.071.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.30 in probability row.
- Locate the value 2 in x column.
- The intersecting value that corresponds to 2 with probability 0.30 is 0.168.
The required probability is,
Hence, the probability of accepting lots that is 30% defective is 0.253.
For 40% defective:
The probability of accepting lots that is 40% defective is,
Compute the probability values for each x using binomial probability distribution table.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.40 in probability row.
- Locate the value 0 in x column.
- The intersecting value that corresponds to 0 with probability 0.40 is 0.002.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.40 in probability row.
- Locate the value 1 in x column.
- The intersecting value that corresponds to 1 with probability 0.40 is 0.017.
From the Appendix B: Tables B.1 Binomial Probability Distribution:
- Select the table with sample size 12.
- Locate the value 0.40 in probability row.
- Locate the value 2 in x column.
- The intersecting value that corresponds to 2 with probability 0.40 is 0.064.
The required probability is,
Hence, the probability of accepting lots that is 40% defective is 0.083.
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Chapter 19 Solutions
Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
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