Poisson Distribution
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Sample
problem: Two hundred fifty-four people take a vacation
from work at CFCC per year. Use the Poisson probability distribution to
calculate the following probabilities.
(a)
Probability that on a randomly selected day 1 person is on vacation. (b) Probability
that on a randomly selected day 4 persons are on vacation. (c) Probability
that on a randomly selected day at most 4 persons are on vacation. (d)
Probability that on a randomly selected day at least 4 persons are on
vacation. Step 1
uses the “poissonpdf(“ function. Step 2 uses the “poissoncdf(” function. |
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Step 1. NOTE: Use poissonpdf when finding the probability that x equals a particular value. Press 2ND VARS. Use the down arrow to select C: poissonpdf(
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(a) After Step 1, Press ENTER. Enter the mean [254/365 people per day on vacation], 1
person on vacation. The probability that one person is on vacation is 0.3470. P(x = 1) = 0.3470. |
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(b) After Step 1, Press ENTER. Enter the mean [254/365 people per day on vacation], 4
persons on vacation. The probability that four persons are on vacation is 0.0049. P(x = 4) = 0.0049. |
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Step 2. NOTE: Use poissoncdf when finding the probability that x is less than or equal to a particular value. Press 2ND VARS. Use the down arrow to select D: poissoncdf(
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(c) After Step 2, Press ENTER. Enter the mean [254/365 people per day on vacation], 4
persons or less on vacation. P(x ≤ 4) = 0.9992. |
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(d) Find P(x ≥ 4) by finding 1 – P(x < 4) = 1 – P(x ≤ 3). Press 1 – poissoncdf(254/365,3) and ENTER. So P(x ≥ 4) = people per day on
vacation], 4 persons or less on vacation. P(x ≤ 4) = 0.9992. |
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