In a manufacturing industry, the amounts which go into raw materials (Scraps) are supposed to be normally distributed with mean GHC 36. and standard deviation GHC 0.1. Once every 30 minutes a scrap is selected from the production line, and its contents are noted precisely. If the amount of the scrap goes below GHC 35.8. or above GHC 36.2, then the scrap will be declared out of control. i. If the process shifts so that μ = GHC 37 and σ = GHC 0.4, find the probability that a scrap will be declared out of control.

Question

In a manufacturing industry, the amounts which go into raw materials (Scraps) are supposed to be normally distributed with mean GHC 36. and standard deviation GHC 0.1. Once every 30 minutes a scrap is selected from the production line, and its contents are noted precisely. If the amount of the scrap goes below GHC 35.8. or above GHC 36.2, then the scrap will be declared out of control.

i. If the process shifts so that μ = GHC 37 and σ = GHC 0.4, find the probability that a scrap will be declared out of control.

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