Grade 10 · Statistics & probability

Normal distribution basics practice

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 15 normal distribution basics problems our math games drill.

CCSS HSS.ID.A.415 questions in the bank
Sample questions

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Question 1easy

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.

Question 2easy

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.

Question 3easy

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.

Question 4easy

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

502×5=4050 - 2\times5 = 40.

Question 5easy

A normal distribution has mean 200200 and standard deviation 2020. What value is 1 standard deviation below the mean?

2001×20=180200 - 1\times20 = 180.

Question 6easy

In a normal distribution, what percent of the data lies above the mean? (Enter percent.)

A normal curve is symmetric about the mean, so 50%50\% lies above it.

Question 7easy

Quiz scores are approximately normally distributed with mean 8080 and standard deviation 44. By the empirical rule, about what percent of scores are between 7272 and 8888? (Enter the number of percent.)

7272 and 8888 are each 2×4=82 \times 4 = 8 points, or 2 standard deviations, from the mean 8080, so by the empirical rule about 95%95\% of scores fall between them.

Question 8easy

For a normal distribution, approximately what percent of data lies more than 2 standard deviations from the mean (counting both tails)? (Use the empirical rule; enter the number of percent.)

About 95%95\% of the data lies within 2 SD of the mean, so 100%95%=5%100\% - 95\% = 5\% lies more than 2 SD away.

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