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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:

    • Never occurring
    • Impossible to measure
    • Always dependent
    • Equally likely to occur
    Reveal answer

    Answer: Equally likely to occur

    Source evidence

    PDF page 318: 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.

  2. The uniform distribution is classified as what type of probability distribution?

    • Categorical
    • Continuous
    • Discrete
    • Binomial
    Reveal answer

    Answer: Continuous

    Source evidence

    PDF page 318: 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.

  3. When working uniform distribution problems, you should note whether the data are:

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

    Answer: Inclusive or exclusive of endpoints

    Source evidence

    PDF page 318: 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.

  4. For the baby smiling example, the distribution is written as:

    • X ~ U(0, 15)
    • X ~ U(6, 15)
    • X ~ U(0, 23)
    • X ~ U(1.5, 4)
    Reveal answer

    Answer: X ~ U(0, 23)

    Source evidence

    PDF page 318: For this example, X ~ U(0, 23) and f(x) =

  5. The smiling times are assumed to follow a uniform distribution between:

    • 1 and 20 seconds
    • 0 and 23 seconds
    • 5 and 25 seconds
    • 0 and 15 seconds
    Reveal answer

    Answer: 0 and 23 seconds

    Source evidence

    PDF page 318: 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

  6. For the baby smiling example, the sample mean is:

    • 7.9
    • 11.49
    • 6.23
    • 4.33
    Reveal answer

    Answer: 11.49

    Source evidence

    PDF page 318: The sample mean = 11.49 and the sample standard deviation = 6.23.

  7. For the baby smiling example, the sample standard deviation is:

    • 11.49
    • 4.33
    • 7.9
    • 6.23
    Reveal answer

    Answer: 6.23

    Source evidence

    PDF page 318: The sample mean = 11.49 and the sample standard deviation = 6.23.

  8. For the charter fishing boat data, the sample mean is:

    • 6.23
    • 11.49
    • 7.9
    • 14
    Reveal answer

    Answer: 7.9

    Source evidence

    PDF page 318: The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of a and b. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

  9. The theoretical mean and standard deviation are described as being:

    • Exactly equal
    • Always zero
    • Far from the sample values
    • Close to the sample values
    Reveal answer

    Answer: Close to the sample values

    Source evidence

    PDF page 318: Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.

  10. For the bus wait example, X is uniformly distributed as:

    • X ~ U(0, 15)
    • X ~ U(1.5, 4)
    • X ~ U(0, 23)
    • X ~ U(6, 15)
    Reveal answer

    Answer: X ~ U(0, 15)

    Source evidence

    PDF page 321: a. Let X = the number of minutes a person must wait for a bus. a = 0 and b = 15. X ~ U(0, 15). Write the probability density

  11. The probability a person waits fewer than 12.5 minutes for a bus is:

    • 0.6
    • 0.8333
    • 0.30
    • 0.90
    Reveal answer

    Answer: 0.8333

    Source evidence

    PDF page 321: The probability a person waits fewer than 12.5 minutes is 0.8333.

  12. On average, how long must a person wait for the bus?

    • 13.5 minutes
    • 7.5 minutes
    • 12.5 minutes
    • 4.3 minutes
    Reveal answer

    Answer: 7.5 minutes

    Source evidence

    PDF page 321: = = 7.5. On the average, a person must wait 7.5 minutes.

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Source

Statistics

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

Original textbook · CC BY 4.0

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