Understanding the Normal Distribution Curve

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| Questions: 20 | Updated: Nov 16, 2025
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1) Approximately what percentage of students scored between 67 and 83?

Explanation

67 and 83 are μ ± 1σ → about 68%.

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About This Quiz
Understanding The Normal Distribution Curve - Quiz

This quiz covers the fundamentals of the normal distribution curve, including understanding the empirical rule and z-scores. You'll calculate percentages of data within certain ranges, estimate cutoffs for specific percentiles, and interpret the symmetry and spread of normal distributions.

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2) Approximately what percentage of students scored above 91?

Explanation

91 is μ + 2σ → area above +2σ ≈ 2.5%.

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3) Approximately what percentage of students scored between 59 and 91?

Explanation

59 and 91 are μ ± 2σ → about 95%.

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4) A student scored 83. What is this score’s z-score?

Explanation

z = (83 − 75)/8 = 8/8 = +1.

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5) Approximately what percentage of students scored below 67?

Explanation

67 is μ − 1σ → area below −1σ ≈ 16%.

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6) If the teacher considers the top 2.5% as “Advanced,” approximately what is the cutoff score?

Explanation

Top 2.5% ≈ μ + 2σ = 75 + 16 = 91.

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7) Which statement best describes the symmetry of a normal distribution?

Explanation

Normal curves are symmetric with mean = median = mode.

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8) In a normal distribution, where do inflection points occur relative to the mean?

Explanation

Inflection points are one standard deviation from the mean.

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9) Two normal distributions have the same mean but different standard deviations. The one with larger standard deviation will:

Explanation

Larger σ spreads out the curve and lowers the peak.

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10) If a normal curve is centered at 100 with σ = 15, which score is farthest below the mean in terms of z-score?

Explanation

z(70) = (70 − 100)/15 = −2 (most below).

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11) Which best estimates the proportion within one standard deviation of the mean in a normal distribution?

Explanation

Empirical rule: about 68% within ±1σ.

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12) The empirical rule states that about 99.7% of data in a normal distribution lies within:

Explanation

99.7% within ±3σ.

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13) If a data set is perfectly normal and symmetric, which is true about the area under the curve to the left of the mean?

Explanation

Symmetry → half the area (50%) lies left of the mean.

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14) Consider two normal curves: Curve A has μ = 60, σ = 4; Curve B has μ = 60, σ = 10. Which statement is true?

Explanation

Larger σ means wider spread and lower peak.

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15) A normally distributed variable has μ = 40 and σ = 5. Approximately what percent of observations are above 50?

Explanation

50 is μ + 2σ → area above +2σ ≈ 2.5%.

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16) In a normal distribution, which statement about tails is correct?

Explanation

Normal tails are infinite and asymptotic.

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17) Which scenario is most appropriate to model with a normal distribution?

Explanation

Human heights are well-approximated by a normal distribution.

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18) A test is normally distributed. A z-score of −2 corresponds to a percentile closest to:

Explanation

z = −2 sits near the 2.5th percentile.

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19) If you increase the standard deviation while keeping the mean constant, which of the following changes?

Explanation

Larger σ → more spread and lower peak; center/area/symmetry unchanged.

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20) For a normal distribution with μ = 200 and σ = 20, which interval captures about 95% of the data?

Explanation

95% ≈ μ ± 2σ → 200 ± 40 → 160 to 240.

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Approximately what percentage of students scored between 67 and 83?
Approximately what percentage of students scored above 91?
Approximately what percentage of students scored between 59 and 91?
A student scored 83. What is this score’s z-score?
Approximately what percentage of students scored below 67?
If the teacher considers the top 2.5% as “Advanced,” approximately...
Which statement best describes the symmetry of a normal distribution?
In a normal distribution, where do inflection points occur relative to...
Two normal distributions have the same mean but different standard...
If a normal curve is centered at 100 with σ = 15, which score is...
Which best estimates the proportion within one standard deviation of...
The empirical rule states that about 99.7% of data in a normal...
If a data set is perfectly normal and symmetric, which is true about...
Consider two normal curves: Curve A has μ = 60, σ = 4; Curve B has...
A normally distributed variable has μ = 40 and σ = 5. Approximately...
In a normal distribution, which statement about tails is correct?
Which scenario is most appropriate to model with a normal...
A test is normally distributed. A z-score of −2 corresponds to a...
If you increase the standard deviation while keeping the mean...
For a normal distribution with μ = 200 and σ = 20, which interval...
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