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Concept explainers
a
Identify the sampling plan that can be preferred, if the seller produces lots with fraction defective
a
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Answer to Problem 183SE
The sampling plan that can be preferred, if the seller produces lots with fraction defective ranging from
Explanation of Solution
Calculation:
Binomial distribution:
A random variable Y is a binomial distribution based on n trails with success
For sampling plan 1 with
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for sampling plan
p | 0.05 | 0.10 | 0.20 | 0.30 | 0.40 |
0.9774 | 0.9186 | 0.7373 | 0.5283 | 0.3370 |
For sampling plan 2 with
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for
The probability of acceptance for sampling plan
p | 0.05 | 0.10 | 0.20 | 0.30 | 0.40 |
0.9987 | 0.9666 | 0.6165 | 0.1934 | 0.02936 |
Step by step procedure to construct OC curve:
- In OC curve, take the values of probability p on x-axis.
- Take the values of probability of acceptance for p on y-axis.
- Locate the value of probability of acceptance 0.0059 corresponding to probability 0.05 for sampling plan 1.
- Similarly locate all the probability values for both the sampling plans.
- Connect all the dots with a curved line to form the OC curve.
The OC curve is,
From the OC curve it can be observed that, for the interval
Hence, the sampling plan that can be preferred, if the seller produces lots with fraction defective ranging from
b
Identify the sampling plan that can be preferred, if the seller produces lots with fraction defective exceeding
b

Answer to Problem 183SE
The sampling plan that can be preferred, if the seller produces lots with fraction defective exceeding
Explanation of Solution
From the OC curve of part (a), it can be observed that, for the p values exceeding 0.30, the line for sampling plan 2 is above the line of sampling plan 1. This shows that, using sampling plan 2 would be preferable if the seller produces lots with fraction defective exceeding 0.30.
Hence, the sampling plan that can be preferred, if the seller produces lots with fraction defective exceeding
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Chapter 3 Solutions
Mathematical Statistics with Applications
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