Answered You can hire a professional tutor to get the answer.
Achieving standards of weight or measure is a problem which faces many companies. This example illustrates the issues involved.
Achieving standards of weight or measure is a problem which faces many companies. This example illustrates the issues involved. One of the many products of a confectionery company is a 250g chocolate bar. The weights of bars produced by the line are known to be Normally distributed - the mean weight, and to a lesser extent the standard deviation, are controllable. The aim of the company is to achieve the specified weight whilst minimising the extent to which the bars are overweight. The standard deviation of weight is currently 2g.
At what level should the mean weight be set to achieve: 95% of production to standard?
99% of production to standard?
In fact, the company must achieve at least 99% of the production to standard. However, they are wondering if they could achieve this more efficiently than with the mean specified above.
The following costs are relevant: A reduction in the mean weight of 1g means a saving to the company of £8 per 1000 bars produced.
To reduce the standard deviation is quite difficult and costly as indicated below:
Standard deviation Cost of achieving
1.5 £10 per 1000 bars
1.25 £20 per 1000 bars
Is there a more cost-effective set-up than the current one?
