The Standard Normal Distribution Quiz
The question sheet
Reveal any answer as you study-
What is the mean of the standard normal distribution?
- Two
- Zero
- One
- Five
Reveal answer
Answer: Zero
Source evidence
PDF page 375: The z-score is three. x − μ The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation z = σ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from a normal distribution with mean μ and standard deviation σ.
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What is the standard deviation of the standard normal distribution?
- Two
- Six
- Zero
- One
Reveal answer
Answer: One
Source evidence
PDF page 375: The z-score is three. x − μ The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation z = σ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from a normal distribution with mean μ and standard deviation σ.
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The transformation z = (x − μ)/σ produces which distribution?
- Z ~ N(0, 1)
- Z ~ N(1, 0)
- Z ~ N(5, 2)
- Z ~ N(μ, σ)
Reveal answer
Answer: Z ~ N(0, 1)
Source evidence
PDF page 375: The z-score is three. x − μ The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation z = σ produces the distribution Z ~ N(0, 1). The value x in the given equation comes from a normal distribution with mean μ and standard deviation σ.
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Values of x larger than the mean have what kind of z-scores?
- Positive z-scores
- Zero z-scores
- Negative z-scores
- Undefined z-scores
Reveal answer
Answer: Positive z-scores
Source evidence
PDF page 375: If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is: x – μ z = σ The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero.
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If x equals the mean, then its z-score is:
- Zero
- One
- Two
- Negative one
Reveal answer
Answer: Zero
Source evidence
PDF page 375: If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is: x – μ z = σ The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero.
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When z is negative, the value x is:
- Undefined
- Equal to μ
- Greater than μ
- Less than μ
Reveal answer
Answer: Less than μ
Source evidence
PDF page 375: μ. Or, when z is positive, x is greater than μ, and when z is negative x is less than μ.
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For X ~ N(5, 6) with x = 17, the z-score equals:
- 6
- –0.67
- 3
- 2
Reveal answer
Answer: 2
Source evidence
PDF page 375: x – μ 17 – 5 z = = = 2 σ 6
PDF page 375: This means that x = 17 is two standard deviations (2σ) above or to the right of the mean μ = 5.
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For X ~ N(5, 2), a weight loss of 10 pounds gives z-score:
- 2.5
- 2.0
- 3.0
- 1.5
Reveal answer
Answer: 2.5
Source evidence
PDF page 375: a. Suppose a person lost ten pounds in a month. The z-score when x = 10 pounds is z = 2.5 (verify). This z-score
PDF page 375: a. This z-score tells you that x = 10 is 2.5 standard deviations to the right of the mean five.
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For X ~ N(5, 2), z = 2.5 tells you x = 10 is to the:
- Right of mean five
- Left of mean ten
- Right of mean two
- Left of mean five
Reveal answer
Answer: Right of mean five
Source evidence
PDF page 375: a. This z-score tells you that x = 10 is 2.5 standard deviations to the right of the mean five.
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For Jerome, X ~ N(16, 4), scoring 10 points gives z-score:
- –4
- 1.5
- 2
- –1.5
Reveal answer
Answer: –1.5
Source evidence
PDF page 376: Jerome averages 16 points a game with a standard deviation of four points. X ~ N(16,4). Suppose Jerome scores ten
PDF page 376: points in a game. The z–score when x = 10 is –1.5. This score tells you that x = 10 is _____ standard deviations to the
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According to the Empirical Rule, about what percent lie within 1σ?
- 68%
- 95%
- 99.7%
- 50%
Reveal answer
Answer: 68%
Source evidence
PDF page 376: • About 68% of the x values lie between –1σ and +1σ of the mean μ (within one standard deviation of the mean).
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About 95% of x values lie within how many standard deviations?
- Two
- Four
- One
- Three
Reveal answer
Answer: Two
Source evidence
PDF page 376: • About 95% of the x values lie between –2σ and +2σ of the mean μ (within two standard deviations of the mean).
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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