Assume the machine shifts and the distribution of the amount of the compound added now has a mean of 9.96 milligrams ans a standard deviation of 0.05 milligram. You select one vial and detrmine how much of the compound was added. Acceptable range of amounts of compound added is 9.65 milligrams to 9.95 milligrams. Original distribution of individual vials mean=9.8 a) What is the probability that you select a vial is within the acceptable range ( in other words, you do not detect that the machine has shifted? b) You randomly select 15 vials. What is the probability that you select one vial that is within the acceptable range?
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!
Assume the machine shifts and the distribution of the amount of the compound added now has a mean of 9.96 milligrams ans a standard deviation of 0.05 milligram. You select one vial and detrmine how much of the compound was added. Acceptable
a) What is the
b) You randomly select 15 vials. What is the probability that you select one vial that is within the acceptable range?
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