You are employed as QA responsible (QA = "Quality Assurance") in a company that producessalmon. Production takes place in a land-based facility where all parameters of productioncan be varied. Recently, challenges have arisen in production and you have been askedto assess the situation.Based on many years of production, it is known that the weight of salmon producedis normally distributed with an expectation of 3 kg and a standard deviation of 0.5 kg.The salmon is transported out of the plant in crates containing 50 salmon.(a) Let X denote the weight of one salmon and K the weight of a case of salmon. The weight of the selfthe case can be neglected. Assume independence between weight of two arbitrary salmon, andfind the expectation and standard deviation for the weight of a box of salmon, respectively µKand σK.(b) Which probability distribution can be used to indicate the weight of a box K?Give reasons for the answer.(c) What must be set as the lower and upper limit in the weight control so that 95% of the boxesto pass the control? (Hint: Spread interval)Note: If you have not completed the earlier tasks, but know what to doin this task, you can use µW = 200 and σW = 4 here.(d) Handling boxes that are rejected in the weigh check is a challenge. (Accordingto the criterion in the previous subtask, the probability of a box being rejected is 5%the control, we will further assume that there is independence between the weights of two arbitraryboxes.) One day 100 boxes of fish are produced. Let W stand for the number of boxes leftrejected at the weight check one day.i. Which probability distribution can be used to describe W? Give reasons for the answer.ii. What is the expectation µW and the standard deviation σW of W (the number of boxes thatrejected within a day)?iii. The finance department has estimated the cost associated with handling cash registerswhich is rejected. A cost of NOK 110 is incurred per rejected boxper day a fixed cost of NOK 1,000 could be calculated to operate the system. Let Ddenote the cost per day. Then D = 110W + 1000. What is the expectation µDand the standard deviation σD of the daily cost?(e) Let Y be the number of the first case rejected at the checkweigher on a day.i. Which probability distribution can be used to describe Y? Justify the answer.ii. What is the probability that at least one of the first 10 boxes is rejected?
You are employed as QA responsible (QA = "Quality Assurance") in a company that produces
salmon. Production takes place in a land-based facility where all parameters of production
can be varied. Recently, challenges have arisen in production and you have been asked
to assess the situation.
Based on many years of production, it is known that the weight of salmon produced
is
The salmon is transported out of the plant in crates containing 50 salmon.
(a) Let X denote the weight of one salmon and K the weight of a case of salmon. The weight of the self
the case can be neglected. Assume independence between weight of two arbitrary salmon, and
find the expectation and standard deviation for the weight of a box of salmon, respectively µK
and σK.
(b) Which
Give reasons for the answer.
(c) What must be set as the lower and upper limit in the weight control so that 95% of the boxes
to pass the control? (Hint: Spread interval)
Note: If you have not completed the earlier tasks, but know what to do
in this task, you can use µW = 200 and σW = 4 here.
(d) Handling boxes that are rejected in the weigh check is a challenge. (According
to the criterion in the previous subtask, the probability of a box being rejected is 5%
the control, we will further assume that there is independence between the weights of two arbitrary
boxes.) One day 100 boxes of fish are produced. Let W stand for the number of boxes left
rejected at the weight check one day.
i. Which probability distribution can be used to describe W? Give reasons for the answer.
ii. What is the expectation µW and the standard deviation σW of W (the number of boxes that
rejected within a day)?
iii. The finance department has estimated the cost associated with handling cash registers
which is rejected. A cost of NOK 110 is incurred per rejected box
per day a fixed cost of NOK 1,000 could be calculated to operate the system. Let D
denote the cost per day. Then D = 110W + 1000. What is the expectation µD
and the standard deviation σD of the daily cost?
(e) Let Y be the number of the first case rejected at the checkweigher on a day.
i. Which probability distribution can be used to describe Y? Justify the answer.
ii. What is the probability that at least one of the first 10 boxes is rejected?
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