Solving Probability of Process: Sketching Functions & Annual Savings

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zaka
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Hi, I'm trying to solve the following question, but unsure how to approach it.

A paper manufacturing process states (in its specifications) that each piece of paper's weight will be less than the nomial weight of 1.2 grams on NO MORE than 1 occasion in 100. Currently, the process produces to any required mean piece of paper weight with a standard deviation of 0.01 grams. A new process is available which makes to a more consistent weight, the standard deviation of weights being 0.008 grams.

Q1) Sketch the functions that model these 2 cases (current and new process).

Both processes can make 20,000 sheets of paper per minute, and will be required to work for a 40 hour week, 50 weeks a year. The price of paper is around £2 per kilogram.

Q2) Find the annual savings made possible by the new process.


For question one, how are the functions stetched? I thought of using normal distribution tables to work out this question by letting Probability(u < 1.2) = 0.01, however nowhere in the question does it state that the process is normally distributed so I think that's wrong (I have no idea how to approach this question as you can tell).

Any help would be much appriciated.
 

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You can assume a normal distribution. This is the usual procedure in problems like this. The trick is to define the mean weight for each of these processes so that for the given standard deviation the probability of light weight is no more than 1%.

The cost saving will be determined by the difference in mean weight between the processes.