The Uniform Distribution Quiz
The question sheet
Reveal any answer as you study-
The uniform distribution is what type of probability distribution?
- Exponential
- Binomial
- Discrete
- Continuous
Reveal answer
Answer: Continuous
Source evidence
PDF page 338: The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data are inclusive or exclusive of endpoints.
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In X ~ U(a, b), what does a represent?
- The mean of x
- The lowest value of x
- The standard deviation
- The highest value of x
Reveal answer
Answer: The lowest value of x
Source evidence
PDF page 339: X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.
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For the baby smiling times, what distribution is assumed?
- U(0, 15)
- U(0, 14)
- U(0, 23)
- U(1.5, 4)
Reveal answer
Answer: U(0, 23)
Source evidence
PDF page 339: We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution. Let X = length, in seconds, of an eight-week-old baby's smile. The notation for the uniform distribution is
PDF page 339: b − a 1 For this example, X ~ U(0, 23) and f(x) =
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For the baby smiling example, the theoretical mean is:
- 6.64 seconds
- 11.50 seconds
- 20.7 seconds
- 11.49 seconds
Reveal answer
Answer: 11.50 seconds
Source evidence
PDF page 339: = 11.50 seconds and σ =
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For the baby smiling example, the theoretical standard deviation is:
- 4.33 seconds
- 6.23 seconds
- 11.50 seconds
- 6.64 seconds
Reveal answer
Answer: 6.64 seconds
Source evidence
PDF page 339: = 6.64 seconds. 2 12 Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.
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What is the 90th percentile for a baby's smiling time?
- 13.5 seconds
- 20.7 seconds
- 18 seconds
- 23 seconds
Reveal answer
Answer: 20.7 seconds
Source evidence
PDF page 341: k = (23)(0.90) = 20.7
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For bus wait time U(0,15), P(x < 12.5) equals:
- 0.5000
- 0.6000
- 0.90
- 0.8333
Reveal answer
Answer: 0.8333
Source evidence
PDF page 342: = 0.8333 ⎝15⎠ The probability a person waits fewer than 12.5 minutes is 0.8333.
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For bus wait time U(0,15), the average wait is:
- 7.5 minutes
- 4.3 minutes
- 12.5 minutes
- 13.5 minutes
Reveal answer
Answer: 7.5 minutes
Source evidence
PDF page 343: = = 7.5. On the average, a person must wait 7.5 minutes. 2 2
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For bus wait time U(0,15), the standard deviation is:
- 13.5 minutes
- 7.5 minutes
- 4.3 minutes
- 0.8333 minutes
Reveal answer
Answer: 4.3 minutes
Source evidence
PDF page 343: = 4.3. The standard deviation is 4.3 minutes. = 12 12
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For bus wait U(0,15), the 90th percentile is:
- 13.5 minutes
- 7.5 minutes
- 20.7 minutes
- 12.5 minutes
Reveal answer
Answer: 13.5 minutes
Source evidence
PDF page 343: k = (0.90)(15) = 13.5
PDF page 343: The 90 percentile is 13.5 minutes. Ninety percent of the time, a person must wait at most 13.5 minutes.
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The 90th percentile k is sometimes called what?
- A modal value
- A mean value
- A median value
- A critical value
Reveal answer
Answer: A critical value
Source evidence
PDF page 343: k is sometimes called a critical value.
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For furnace repair U(1.5,4), P(x > 2) equals:
- 0.8
- 0.4
- 0.3
- 0.6
Reveal answer
Answer: 0.8
Source evidence
PDF page 346: P(x > 2) = (base)(height) = (4 – 2)(0.4) = 0.8
High School Statistics
High School Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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