OpenStax, Introductory Statistics 2e §4.6 Poisson Distribution · Exercise 20 · Probability · Discrete distributions

Poisson Distribution · Exercise 20

The chance of having an extra fortune in a fortune cookie is about 3%. Given a bag of 144 fortune cookies, we are interested in the number of cookies with an extra fortune. Two distributions may be used to solve this problem, but only use one distribution to solve the problem.

(a) In words, define the random variable X.
(b) List the values that X may take on.
(c) Give the distribution of X. X ~ _____(_____,_____)
(d) How many cookies do we expect to have an extra fortune?
(e) Find the probability that none of the cookies have an extra fortune.
(f) Find the probability that more than three have an extra fortune.
(g) As n increases, what happens involving the probabilities using the two distributions? Explain in complete sentences.

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OpenStax, Introductory Statistics 2e · §4.6 Poisson Distribution · Exercise 20

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