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Binomial & Poisson Distributions · Question 63 of 68

What is the probability that the helpline gets at most one call in a 5-minute spell?

Question 63

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 at most one call in a 5-minute spell?

Options for question 63

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(X≤1)=e−3+3e−3=4e−3P(X \le 1) = e^{-3} + 3e^{-3} = 4e^{-3}.

  2. 4×0.0498=0.19924 \times 0.0498 = 0.1992.

Worth noting

0.1494 is exactly one call; 'at most one' takes in no call as well.

Concept
Adding Poisson probabilities
Typical time
120 s
Your time
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The rule this testsThe Poisson distribution
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