Question

3.2 measures of spread: empirical rule
the mean gpa for 50 students was 3.02 and the standard deviation was 0.3. assume that the distribution of gpas is unimodal and symmetric.
the percentage of data that occurs within one standard deviation of the mean should be select an answer
the percentage of data that occurs within two standard deviations of the mean should be select an answer
the percentage of data that occurs within three standard deviations of the mean should be select an answer
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Explanation:

Step1: Recall empirical rule

The empirical rule for a unimodal and symmetric (normal - like) distribution states certain percentages of data within standard - deviation ranges of the mean.

Step2: Percentage within one standard deviation

For a normal distribution, approximately 68% of the data lies within one standard deviation of the mean.

Step3: Percentage within two standard deviations

Approximately 95% of the data lies within two standard deviations of the mean.

Step4: Percentage within three standard deviations

Approximately 99.7% of the data lies within three standard deviations of the mean.

Answer:

The percentage of data that occurs within one standard deviation of the mean should be 68%.
The percentage of data that occurs within two standard deviations of the mean should be 95%.
The percentage of data that occurs within three standard deviations of the mean should be 99.7%.