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Binomial & Poisson Distributions · Question 61 of 68

Question 61

MediumOriginal question

2% of the pens a machine makes are faulty. Using the Poisson distribution, what is the probability that a pack of 100 pens has no faulty pen? (Take e−2=0.1353e^{-2} = 0.1353.)

Options for question 61

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. λ=np=100×0.02=2\lambda = np = 100 \times 0.02 = 2.

  2. P(X=0)=e−2=0.1353P(X = 0) = e^{-2} = 0.1353.

Worth noting

0.98 is the chance that one pen is good, not all 100.

Concept
Poisson as an approximation to the binomial
Typical time
90 s
Your time
—
The rule this testsThe Poisson distribution
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Ten questions from Binomial & Poisson Distributions, at your own pace.

Practise this chapter →

Ten questions from Binomial & Poisson Distributions, at your own pace.