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1.05 Interpreting and comparing z-scores

Interactive practice questions

Complete the following statements for a normal distribution using the empirical rule.

a

$\editable{}$$%$% of the scores lie within $1$1 standard deviation of the mean.

b

$\editable{}$$%$% of the scores lie within $2$2 standard deviations of the mean.

c

$\editable{}$$%$% of the scores lie within $3$3 standard deviations of the mean.

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In a normal distribution, what percentage of scores lie between the mean and $1$1 standard deviation above the mean? Use the empirical rule to find your answer.

In a normal distribution, what percentage of scores lie between the mean and $2$2 standard deviations below the mean? Use the empirical rule to find your answer.

Consider the normal distribution shown below. Each unit on the horizontal axis indicates $1$1 standard deviation.

Outcomes

S.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. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

S.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S.IC.B.5

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

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