Assume that X is a Poisson random variable with 24 Calculat

Assume that X is a Poisson random variable with = 24. Calculate the following probabilities. (Round your intermediate calculations and final answers to 4 decimal places.)

Solution

Note that in case you are using technology, you can use the POISSON.DIST(x value, mean, cumulative) function to solve this.

Cumulative = 0 if you want exactly x successes, and 1 if you want at most x successes.

If you don\'t use technology, please disregard the Excel functions, and use your table normally.

a)

Using a table or technology, as u = 24,

=POISSON.DIST(18,24,1)

P(x<=18) = 0.128278703 [ANSWER]

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b)

Here,

P(x = 22)

=POISSON.DIST(22,24,0)

=0.07777019 [ANSWER]

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c)

Here, note that

P(x>24) = 1 - P(x<=23)

=1 - POISSON.DIST(23,24,1)

= 0.527150279 [answer]

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d)

Note that

P(21<=x<=31) = P(x<=31) - P(x<=20)

= POISSON.DIST(31,24,1) - POISSON.DIST(20,24,1)

=0.689596923 [answer]