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The Uniform Distribution Quiz

12 questions math Grades 9-12

The question sheet

Reveal any answer as you study

  1. The uniform distribution is concerned with events that are:

    • Equally likely to occur
    • Always increasing
    • Mutually exclusive
    • Rare and unpredictable
    Reveal answer

    Answer: Equally likely to occur

    Source evidence

    PDF page 324: 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 is inclusive or exclusive of endpoints.

  2. The uniform distribution is which type of probability distribution?

    • Discrete
    • Geometric
    • Continuous
    • Binomial
    Reveal answer

    Answer: Continuous

    Source evidence

    PDF page 324: 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 is inclusive or exclusive of endpoints.

  3. When solving uniform distribution problems, you should note whether the data is:

    • Rounded or exact
    • Inclusive or exclusive of endpoints
    • Positive or negative
    • Sorted or unsorted
    Reveal answer

    Answer: Inclusive or exclusive of endpoints

    Source evidence

    PDF page 324: 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 is inclusive or exclusive of endpoints.

  4. In the notation X ~ U(a, b), what does a represent?

    • The mean
    • 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 325: X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.

  5. For the baby smiling example, the smiling times follow a uniform distribution between:

    • 0 and 15 seconds
    • 0 and 23 seconds
    • 0 and 20 seconds
    • 1 and 22 seconds
    Reveal answer

    Answer: 0 and 23 seconds

    Source evidence

    PDF page 325: 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 325: b − a 1 For this example, X ~ U(0, 23) and f(x) =

  6. For the smiling example X ~ U(0, 23), the theoretical mean is about:

    • 20.7 seconds
    • 6.64 seconds
    • 11.50 seconds
    • 11.49 seconds
    Reveal answer

    Answer: 11.50 seconds

    Source evidence

    PDF page 325: = 11.50 seconds and σ =

  7. For X ~ U(0, 23), the theoretical standard deviation is about:

    • 11.50 seconds
    • 6.23 seconds
    • 4.33 seconds
    • 6.64 seconds
    Reveal answer

    Answer: 6.64 seconds

    Source evidence

    PDF page 325: = 6.64 seconds. 12 2 Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.

  8. The 90th percentile for the baby smiling time (X~U(0,23)) is:

    • 18 seconds
    • 23 seconds
    • 20.7 seconds
    • 12 seconds
    Reveal answer

    Answer: 20.7 seconds

    Source evidence

    PDF page 327: k = (23)(0.90) = 20.7

  9. For the bus wait X ~ U(0, 15), the probability a person waits fewer than 12.5 minutes is:

    • 0.9000
    • 0.8333
    • 0.5000
    • 0.6250
    Reveal answer

    Answer: 0.8333

    Source evidence

    PDF page 328: 15 − 0 15 Find P (x < 12.5). Draw a graph. ⎛ 1 ⎞ = 0.8333

    PDF page 328: ⎝15⎠ The probability a person waits less than 12.5 minutes is 0.8333.

  10. For the bus wait X ~ U(0, 15), the average waiting time is:

    • 4.3 minutes
    • 15 minutes
    • 13.5 minutes
    • 7.5 minutes
    Reveal answer

    Answer: 7.5 minutes

    Source evidence

    PDF page 329: = = 7.5. On the average, a person must wait 7.5 minutes. 2 2

  11. For the bus wait X ~ U(0, 15), the standard deviation is:

    • 4.3 minutes
    • 6.64 minutes
    • 7.5 minutes
    • 13.5 minutes
    Reveal answer

    Answer: 4.3 minutes

    Source evidence

    PDF page 329: (b - a) (15 - 0) = = 4.3. The Standard deviation is 4.3 minutes.

  12. For the bus wait X ~ U(0, 15), the 90th percentile is:

    • 15 minutes
    • 12.5 minutes
    • 13.5 minutes
    • 7.5 minutes
    Reveal answer

    Answer: 13.5 minutes

    Source evidence

    PDF page 329: k = (0.90)(15) = 13.5

    PDF page 329: 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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Source

Introductory Statistics

Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.

Original textbook · CC BY 4.0

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