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Binomial & Poisson Distributions · Question 64 of 68

What is the probability that the helpline gets exactly 2 calls in a 5-minute spell?

Question 64

MediumOriginal question

A helpline receives calls at an average of 3 every 5 minutes, following a Poisson distribution. (Take e−3=0.0498e^{-3} = 0.0498.)

What is the probability that the helpline gets exactly 2 calls in a 5-minute spell?

Options for question 64

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. P(X=2)=e−3×322!P(X = 2) = \frac{e^{-3} \times 3^{2}}{2!}.

  2. 4.5×0.0498=0.22414.5 \times 0.0498 = 0.2241.

Worth noting

0.4482 forgets to divide by 2!=22! = 2.

Concept
The probability of exactly r events
Typical time
120 s
Your time
—
The rule this testsThe Poisson distribution
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