Correct Fish Weight: In the plant, fish are made into blocks of “about” 10 kg each.
In fish processing plant, after fish are brought from sea, they are made into blocks of “about” 10 kg each. Then these blocks are frozen in blast freezers, and sent to customers. Customers thaw blocks at their end.
Weight loss occurs at two stages viz. freezing and thawing.
Randomly chosen 100 blocks of fish (of single/uniform grade) were observed for freezing loss at fish processing plant.
Customer sent observations of randomly chosen 100 blocks (of same grade as that at fish processing plant) for thawing loss.
Following are the observations
Weight loss in freezing
Average: 1%
Std dev : 0.25%
Weight loss in thawing (drip loss)
Average: 4%
Std dev : 0.5%
Fish blocks are prepared in batches. 1000 blocks per batch.
Question : After thawing, weight of fish block should be least of 10 kg. What should be minimum weight (wet weight/fresh weight) of fish blocks so that no more than 10 % of thawed fish blocks are found to be short weight (i.e. less than 10 kg) by customer. Total number of blocks 10,000.
a) Assume there is no correlation (zero correlation) between freezing loss and thawing loss.
b) Assume there is perfect correlation (1correlation) between freezing loss and thawing loss.
How to go about it ?
I have tried to solve it in following way. I am not sure it is correct.
Step1.
Step 2.
Calculate 95% confidence limit for population mean for both; freezing loss and thawing loss.
Step 3
. Calculate 90th percentile for both by presuming UCL as mean (liberal attitude)
Step 4
Target weight after thawing is (min) 10.0 kg
Ans : Thus, minimum weight (wet weight/fresh weight) of fish blocks so that no more than 10 % of thawed fish blocks are found to be short weight (i.e. less than 10 kg) by customer is 10.643 kg. I have not taken in to account correlation in this solution.
Is it correct ? If not, what changes are required ?
In fish processing plant, after fish are brought from sea, they are made into blocks of “about” 10 kg each. Then these blocks are frozen in blast freezers, and sent to customers. Customers thaw blocks at their end.
Weight loss occurs at two stages viz. freezing and thawing.
Randomly chosen 100 blocks of fish (of single/uniform grade) were observed for freezing loss at fish processing plant.
Customer sent observations of randomly chosen 100 blocks (of same grade as that at fish processing plant) for thawing loss.
Following are the observations
Weight loss in freezing
Average: 1%
Std dev : 0.25%
Weight loss in thawing (drip loss)
Average: 4%
Std dev : 0.5%
Fish blocks are prepared in batches. 1000 blocks per batch.
Question : After thawing, weight of fish block should be least of 10 kg. What should be minimum weight (wet weight/fresh weight) of fish blocks so that no more than 10 % of thawed fish blocks are found to be short weight (i.e. less than 10 kg) by customer. Total number of blocks 10,000.
a) Assume there is no correlation (zero correlation) between freezing loss and thawing loss.
b) Assume there is perfect correlation (1correlation) between freezing loss and thawing loss.
How to go about it ?
I have tried to solve it in following way. I am not sure it is correct.
Step1.
| | Average (%) | Standard deviation (%) |
| Freezing loss | 1.0 | 0.25 |
| Thawing loss | 4.0 | 0.5 |
Step 2.
Calculate 95% confidence limit for population mean for both; freezing loss and thawing loss.
| | Lower Confidence Limit | Upper Confidence Limit |
| Freezing loss | 0.951 | 1.049 |
| Thawing loss | 3.902 | 4.098 |
Step 3
. Calculate 90th percentile for both by presuming UCL as mean (liberal attitude)
| | Freezing loss % | Thawing loss % |
| 90th percentile | 1.36939 | 4.739 |
Step 4
Target weight after thawing is (min) 10.0 kg
| 10.00 | thawed weight |
| 10.50 | frozen weight (dividing 10 by (1-0.0136939) |
| 10.643 | fresh weight (dividing 10.5 by(1-0.04739) |
Ans : Thus, minimum weight (wet weight/fresh weight) of fish blocks so that no more than 10 % of thawed fish blocks are found to be short weight (i.e. less than 10 kg) by customer is 10.643 kg. I have not taken in to account correlation in this solution.
Is it correct ? If not, what changes are required ?