is selected from the production line, and its contents are noted precisely. If the amount of the bag goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control. a) If the process is in control, meaning µ = 36 kg and = 0.1 kg, find the probability that the bag will be declared out of control. b) In the situation of (a), find the probability that the number of bag fou
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!
At QT Sugar factory the amounts which go into bag of sugar are supposed to be
distributed
selected from the production line, and its contents are noted precisely. If the amount of the bag
goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control.
a) If the process is in control, meaning µ = 36 kg and = 0.1 kg, find the probability that the bag
will be declared out of control.
b) In the situation of (a), find the probability that the number of bag found out of control in an
eight-hour day (16 inspections) will be zero.
c) In the situation of (a), find the probability that the number of bag found out control in an eighthour day (16 inspections) will be exactly one.
d) If the process shifts so that µ =37 kg and =0.4 kg find the probability that a bag will be
declared out of control.
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