Normal distribution basics. Game on.

Normal distribution basics is a grade 10 math skill aligned to Common Core standard HSS.ID.A.4: use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 26 normal distribution basics problems our math games drill.

CCSS HSS.ID.A.426 questions in the bank
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Warm-upeasy

For a normal distribution, approximately what percent of the data lies within 22 standard deviations of the mean? Use the empirical rule.

By the empirical rule, about 95%95\% of the data lie within 22 standard deviations of the mean.

Mid-gameeasy

For a normal distribution, approximately what percent of data lies within 2 standard deviations of the mean? (Use the empirical rule; enter the number of percent.)

By the empirical rule, about 95%95\% lies within 2 SD of the mean.

Mid-gameeasy

For a normal distribution, approximately what percent of the data lies within 33 standard deviations of the mean? Use the empirical rule.

By the empirical rule, about 99.7%99.7\% of the data lie within 33 standard deviations of the mean.

Mid-gameeasy

For a normal distribution, approximately what percent of data lies within 3 standard deviations of the mean? (Use the empirical rule; enter the number of percent.)

By the empirical rule, about 99.7%99.7\% lies within 3 SD of the mean.

Mid-gameeasy

A normal distribution has mean 5050 and standard deviation 5.5\textsf{.} What value is 22 standard deviations below the mean?

50−2×5=40.50 - 2 \times 5 = 40\textsf{.}

Mid-gameeasy

A normal distribution has mean 100100 and standard deviation 1515. What value is 1 standard deviation above the mean?

100+1×15=115100 + 1\times15 = 115.

Mid-gameeasy

In a normal distribution, what percent of the data lies above the mean?

A normal curve is symmetric about the mean, so 50%50\% of the data lie above the mean.

Buzzer beatereasy

A normal distribution has mean 5050 and standard deviation 55. What value is 2 standard deviation below the mean?

50−2×5=4050 - 2\times5 = 40.

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Tests that cover normal distribution basics:
NAEPSBACACTVTCAPNY State Math
Reporting domains for this skill
ACT All grades: Preparing for Higher MathMAP Growth Math 6+: Statistics and ProbabilitySBAC High School: Concepts and ProceduresNAEP Grade 12: Data Analysis, Statistics, and ProbabilityACT Aspire All grades: Integrating Essential SkillsACT Aspire All grades: Preparing for Higher Math
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