A company manufacturing crank case is interested in controlling the weight of crank cases. For better operational performance, slight under weight, if exists due to process variance, may be tolerable. The company would like all crank cases to have a mean weight of 250 kg or less. The company wants to have a plan that will accept lots of such crank cases 90% of the time. It further wants to accept lots having a mean weight of 252 kg or greater with 8% of the time. Assume the population standard deviation of weight of the crank cases as 5 kg. Any shift in the process mean between 250 kg and 252 kg will not affect the performance of the engine. Design a suitable single sampling plan, (i.e. find the sample size and the cut-off value for weight which will help in accepting/rejecting a lot).

AppendixLO1