Poisson Distribution (Optional) Quiz
The question sheet
Reveal any answer as you study-
In the book editor example, what is the interval of interest?
- 100 pages
- One book
- 5 words
- 50 pages
Reveal answer
Answer: 100 pages
Source evidence
PDF page 269: 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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In the bakery example, the time interval of interest is:
- Five minutes
- 30 minutes
- 12 minutes
- One hour
Reveal answer
Answer: Five minutes
Source evidence
PDF page 270: The average number of loaves of bread put on a shelf in a bakery in a half-hour period is 12. Of interest is the number of loaves of bread put on the shelf in five minutes. The time interval of interest is five minutes. What is the probability that the number of loaves, selected randomly, put on the shelf in five minutes is three? Let X = the number of loaves of bread put on the shelf in five minutes. If the average number of loaves put on the shelf in 30 minutes (half-hour) is 12, then the average number of loaves put on the shelf in five minutes is
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For the bakery bread example, the probability question asks you to find:
- P(x > 3)
- P(x = 3)
- P(x < 3)
- P(x = 12)
Reveal answer
Answer: P(x = 3)
Source evidence
PDF page 270: of bread. The probability question asks you to find P(x = 3).
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For the bank bad-check example, the probability question is written as:
- P(x = 5)
- P(x < 5)
- P(x = 6)
- P(x > 5)
Reveal answer
Answer: P(x < 5)
Source evidence
PDF page 270: Problem 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. Solution P(x < 5)
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For the electronics store, X represents the number of returns received in:
- One week
- One hour
- Eight days
- One day
Reveal answer
Answer: One day
Source evidence
PDF page 270: An electronics store expects to have 10 returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day. State the probability question mathematically.
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In the Poisson notation, the parameter μ (or λ) represents the:
- Standard deviation
- Probability of success
- Number of trials
- Mean for the interval of interest
Reveal answer
Answer: Mean for the interval of interest
Source evidence
PDF page 271: 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 271: interval of interest.
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For Leah's calls, what values does X take on?
- 1, 2, 3 only
- 0.75 to 6
- 0, 1, 2, 3, ...
- 0 or 1 only
Reveal answer
Answer: 0, 1, 2, 3, ...
Source evidence
PDF page 271: 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
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In Leah's answering machine example, the value of μ used is:
- 6
- 2
- 1.5
- 0.75
Reveal answer
Answer: 0.75
Source evidence
PDF page 271: (6) = .75 calls in 15 minutes, on average. So, μ = .75 for this problem.
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For Leah's problem, X ~ P(.75) and P(x > 1) equals about:
- 0.75
- 0.5005
- 0.1734
- 0.2505
Reveal answer
Answer: 0.1734
Source evidence
PDF page 271: X ~ P(.75) Find P(x > 1). P(x > 1) = .1734 (calculator or computer) Note The TI calculators use λ (lambda) for the mean.
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The ER example is a Poisson distribution because it concerns:
- The number of doctors
- The cost of treatment
- The distance patients travel
- The number of patients per hour
Reveal answer
Answer: The number of patients per hour
Source evidence
PDF page 271: An emergency room at a particular hospital gets an average of five patients per hour. A doctor wants to know the probability that the ER gets more than five patients per hour. Give the reason why this would be a Poisson distribution.
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For the email user example, the random variable X has which distribution?
- X ~ G(147)
- X ~ N(147)
- X ~ P(147)
- X ~ B(147)
Reveal answer
Answer: X ~ P(147)
Source evidence
PDF page 272: According to Baydin, an email management company, an email user gets, on average, 147 emails per day. Let X = the number of emails an email user receives per day. The discrete random variable X takes on the values x = 0, 1, 2 . . . . The random variable X has a Poisson distribution: X ~ P(147). The mean is 147 emails. Problem
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For the email user, P(x = 160) is calculated using which command?
- poissonpdf(147, 160)
- binompdf(147, 160)
- poissoncdf(147, 160)
- normalcdf(147, 160)
Reveal answer
Answer: poissonpdf(147, 160)
Source evidence
PDF page 272: a. P(x = 160) = poissonpdf(147, 160) ≈ .0180
Statistics
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