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Binomial & Poisson Distributions · Question 53 of 68

What is the probability that the helpline gets no call in a 5-minute spell?

Question 53

EasyOriginal 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 no call in a 5-minute spell?

Options for question 53

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. λ=3\lambda = 3 for a 5-minute spell.

  2. P(X=0)=e−3=0.0498P(X = 0) = e^{-3} = 0.0498.

Worth noting

0.9502 is the chance of at least one call.

Concept
The probability of no event
Typical time
90 s
Your time
—
The rule this testsThe Poisson distribution
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