Poisson Distribution Quiz
The question sheet
Reveal any answer as you study-
For the book editor example, what is the interval of interest?
- One chapter
- One book
- Five words
- 100 pages
Reveal answer
Answer: 100 pages
Source evidence
PDF page 274: time or space if these events happen with a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on the average, there are five words spelled incorrectly in 100 pages. The interval is the 100 pages.
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The parameter of the Poisson distribution is written as:
- μ (or λ)
- p
- n
- σ²
Reveal answer
Answer: μ (or λ)
Source evidence
PDF page 276: Read this as "X is a random variable with a Poisson distribution." The parameter is μ (or λ); μ (or λ) = the mean for the
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The parameter μ (or λ) equals the mean for what?
- The success probability
- The interval of interest
- The number of trials
- The population
Reveal answer
Answer: The interval of interest
Source evidence
PDF page 276: Read this as "X is a random variable with a Poisson distribution." The parameter is μ (or λ); μ (or λ) = the mean for the
PDF page 276: interval of interest.
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For the bakery loaf problem, the probability question asks you to find:
- P(x = 2)
- P(x = 3)
- P(x > 3)
- P(x < 3)
Reveal answer
Answer: P(x = 3)
Source evidence
PDF page 275: ⎝30⎠ The probability question asks you to find P(x = 3).
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A bank expects six bad checks per day. The probability question P(x < 5) means:
- Exactly five bad checks
- Fewer than five bad checks
- At least five bad checks
- More than five bad checks
Reveal answer
Answer: Fewer than five bad checks
Source evidence
PDF page 275: A bank expects to receive six bad checks per day, on average. What is the probability of the bank getting fewer than five bad checks on any given day? Of interest is the number of checks the bank receives in one day, so the time interval of interest is one day. Let X = the number of bad checks the bank receives in one day. If the bank expects to receive six bad checks per day then the average is six checks per day. Write a mathematical statement for the probability question.
PDF page 275: Solution 4.27 P(x < 5)
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Why is the news reporter 'uh' example a Poisson problem?
- You count occurrences during a broadcast
- It uses replacement
- It compares two means
- It uses paired samples
Reveal answer
Answer: You count occurrences during a broadcast
Source evidence
PDF page 275: You notice that a news reporter says "uh," on average, two times per broadcast. What is the probability that the news reporter says "uh" more than two times per broadcast. This is a Poisson problem because you are interested in knowing the number of times the news reporter says "uh" during a broadcast.
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For Leah's answering machine, the mean number of calls in 15 minutes is:
- 1.734
- 0.1734
- 6
- 0.75
Reveal answer
Answer: 0.75
Source evidence
PDF page 276: Leah's answering machine receives about six telephone calls between 8 a.m. and 10 a.m. What is the probability that Leah receives more than one call in the next 15 minutes? 1 Let X = the number of calls Leah receives in 15 minutes. (The interval of interest is 15 minutes or hour.) 4 x = 0, 1, 2, 3, ... If Leah receives, on the average, six telephone calls in two hours, and there are eight 15 minute intervals in two hours, then Leah receives ⎛1⎞
PDF page 276: (6) = 0.75 calls in 15 minutes, on average. So, μ = 0.75 for this problem.
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For Leah's example X ~ P(0.75), the probability P(x > 1) is about:
- 0.75
- 0.1734
- 0.8666
- 0.0180
Reveal answer
Answer: 0.1734
Source evidence
PDF page 276: ⎝8⎠ X ~ P(0.75) Find P(x > 1). P(x > 1) = 0.1734 (calculator or computer)
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For the email user with X ~ P(147), the probability of exactly 160 emails per day is about:
- 0.0180
- 0.8666
- 0.1734
- 12.1244
Reveal answer
Answer: 0.0180
Source evidence
PDF page 277: a. P(x = 160) = poissonpdf(147, 160) ≈ 0.0180
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For X ~ P(147), the probability of at most 160 emails per day is about:
- 0.2505
- 0.2653
- 0.8666
- 0.0180
Reveal answer
Answer: 0.8666
Source evidence
PDF page 277: b. P(x ≤ 160) = poissoncdf(147, 160) ≈ 0.8666
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For the email user example X ~ P(147), the standard deviation is about:
- 12.1244
- 1.7292
- 0.8666
- 147
Reveal answer
Answer: 12.1244
Source evidence
PDF page 278: c. Standard Deviation = σ = μ = 147 ≈ 12.1244
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For a text user averaging 41.5 texts per day, the mean texts per hour is about:
- 24
- 41.5
- 1.7292
- 0.2653
Reveal answer
Answer: 1.7292
Source evidence
PDF page 278: a. Let X = the number of texts that a user sends or receives in one hour. The average number of texts received
PDF page 278: 41.5 ≈ 1.7292. per hour is 24
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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