Goodtaste Ltd., a coffee manufacturer, has recently been prosecuted for selling an underweight 100g jar of coffee. You have been asked to give assistance to the quality control manager who is investigating the problem. Jars are filled automatically and the filling machine can be preset to any desired weight. For the 100g jars of coffee a weight of 101g is set. There is no subsequent checking of the weight of individual jars , although samples are occasionally taken to check for quality. The standard deviation will depend to a certain extent on the mean weight, but for weights between 90g and 110g it is virtually constant at 1.5g. You have been asked to apply your knowledge of the normal distribution to the problem. In particular you have been told that prosecution only occurs when the product is underweight by more than 2%, so you need to find the probability that such a weight could happen by chance. (a) Assuming that the mean weight is 101g, what proportion of jars are: (i) Under 100g in weight? (ii) Under 98g in wieght? (iii) Under 97g in weight? (iv) Over 100g? (b) What should the mean weight be set to in order that the probability of a jar weighing less than 98g is less than 0.1%?
Goodtaste Ltd., a coffee manufacturer, has recently been prosecuted for selling an
underweight 100g jar of coffee. You have been asked to give assistance to the quality
control manager who is investigating the problem.
Jars are filled automatically and the filling machine can be preset to any desired
weight. For the 100g jars of coffee a weight of 101g is set. There is no subsequent
checking of the weight of individual jars , although samples are occasionally taken to
check for quality. The standard deviation will depend to a certain extent on the mean
weight, but for weights between 90g and 110g it is virtually constant at 1.5g.
You have been asked to apply your knowledge of the
problem. In particular you have been told that prosecution only occurs when the
product is underweight by more than 2%, so you need to find the probability that such
a weight could happen by chance.
(a) Assuming that the mean weight is 101g, what proportion of jars are:
(i) Under 100g in weight?
(ii) Under 98g in wieght?
(iii) Under 97g in weight?
(iv) Over 100g?
(b) What should the mean weight be set to in order that the probability of a jar
weighing less than 98g is less than 0.1%?
(c) Write a short note to the Quality Control Manager summarising your results.
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