The packaging process in a breakfast cereal startup company has been adjusted so that an average net weight of 13.0 ounces of cereal is placed in each package. The standard deviation of the actual net weight is 0.1 ounces, and the variation follows a normal distribution. Determine the probability that a randomly chosen package will contain between 12.9 and 13.2 ounces of cereal. Include an illustration of the graph with your answer.
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!
The packaging process in a breakfast cereal startup company has been
adjusted so that an average net weight of 13.0 ounces of cereal is placed in each package. The standard
deviation of the actual net weight is 0.1 ounces, and the variation follows a normal distribution.
Determine the
of cereal. Include an illustration of the graph with your answer.
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