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Poisson Distributions
Let X be a random variable following a Poisson distribution. All Poisson distributions have just one parameter: average rate, λ (lambda). For this problem, let X have rate parameter λ = 14.33. An example of where such a distribution may arise is the following:
Statistics, Inc., makes candy. Unfortunately, they are not too good at it. Every week, an average of 14.33 pieces are defective. These defective pieces will not kill a person, but they will cause the person’s left index finger to turn scarlet. Let X be the number of defective pieces of candy manufactured in a specified week.
From the description, we can tell that X follows a Poisson distribution with rate parameter λ = 14.33. We know X follows a Poisson distribution because it is the number of successes measured over time (or space).
For those who like pictures, here is a graphic of the probability mass function of X. Note that it is skewed positive (right), that its sample space is non-negative, and that there is no upper bound to its sample space. In other words, S = {0, 1, 2, …}.
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Continuing the candy example, let us determine the probability that there is no more than one piece of sour apple candy in the bag. In symbols, calculate P[X ≤ 1].
In the box below, please enter the value of P[X ≤ 1], where X ~ Poisson(λ = 14.33), then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
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