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 is in control, meaning μ = GHC 36.00. and σ = GHC.0.1, find the probability that a scrap will be declared out of control.  ii) In the situation of (i), find the probability that the number of scraps found out of control in an 8hrs day (16 inspections) will be zero.  iii) In the situation of (i), find the probability that the number of scraps found out of control in an 8hrs day (16 inspections) will be exactly one.  iv) 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 is in control, meaning μ = GHC 36.00. and σ = GHC.0.1, find the
probability that a scrap will be declared out of control. 
ii) In the situation of (i), find the probability that the number of scraps found out of
control in an 8hrs day (16 inspections) will be zero. 
iii) In the situation of (i), find the probability that the number of scraps found out of
control in an 8hrs day (16 inspections) will be exactly one. 
iv) 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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