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The number of different mathematics courses at community colleges has a Poisson Distribution with a mean of 20 courses per college.*show your basic keystrokes and round your answer to 4 decimal places.What is the probability there will be exactly 24 courses at a college?What is the probability there will be fewer than 38 courses at 2 colleges?

Question

The number of different mathematics courses at community colleges has a Poisson Distribution with a mean of 20 courses per college.

*show your basic keystrokes and round your answer to 4 decimal places.

  1. What is the probability there will be exactly 24 courses at a college?
  2. What is the probability there will be fewer than 38 courses at 2 colleges?
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Step 1
  1. Probability that there will be exactly 24 courses at a college:

The given information is that the number of different mathematics courses at community colleges has Poisson distribution with mean 20 courses per college.

The probability distribution of a Poisson random variable X with mean λ is given by,

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Step 2

Let the random variable X denote the number of different mathematics courses at community colleges. The n, the probability that there will be exactly 24 courses at a college is as obtained as follows:

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Step 3

Thus, the probability that there will be exactly 24 co...

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