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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In a manufacturing industry, the amounts which go into raw materials (Scraps) are
supposed to be
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
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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