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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

What percentage of the scores lie within $1$1 standard deviation of the mean?

$34%$34%

A

$68%$68%

B

$32%$32%

C

$99.7%$99.7%

D

$95%$95%

E
b

What percentage of the scores lie within $2$2 standard deviations of the mean?

$99.7%$99.7%

A

$95%$95%

B

$5%$5%

C

$47.5%$47.5%

D

$68%$68%

E
c

What percentage of the scores lie within $3$3 standard deviations of the mean?

$95%$95%

A

$99.7%$99.7%

B

$49.85%$49.85%

C

$68%$68%

D

$0.03%$0.03%

E
Easy
1min

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.

Easy
< 1min

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.

Easy
< 1min

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

Easy
< 1min
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Outcomes

III.S.ID.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.

III.S.IC.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.

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