22) The company uses its excess chips and sawdust as furnish for the manufacture of particleboard....

22) The company uses its excess chips and sawdust as furnish for the manufacture of particleboard. The particleboard plant has a variable forming machine that discharges furnish in amounts that are normally distributed with a mean, μ kg, and a standard deviation of 2.57 kg. If the company wishes to use the forming machine to fill a forming belt that holds a maximum of 200 kg of furnish at once and only wants to overfill the forming belt 1% of the time, at what value of μ should the company set its forming machine?

Expert Solution

Let X kg be the amount furnish discharged on any given fill. X has a normal distribution with a mean μ kg, and a standard deviation of

We want the forming machine to fill a forming belt that holds a maximum of 200 kg of furnish at once and only wants to overfill the forming belt 1% of the time. This is same as, we want the the probability that the forming machine fills more than 200 kg to be 0.01

The z values corresponding to 0.01 is

Using the standard normal tables, we get for z=2.33, P(Z<2.33)=0.99

Hence

We need

We can equate the z score of 200 to 2.33 and get

ans: The value of μ the company should set its forming machine at is 194.01 kg (rounded to 2 decimals)

orchestra answered 1 year ago

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