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1.5 SD = 1.5 * 0.6 = 0.9

The range will be
2.95 - 0.9 = 2.05 and 2.95 + 0.9 = 3.85

4 values,,option E
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This problem tests your understanding of how the standard deviation is used within a set of data. Because the standard deviation is 0.6, then 1.5 standard deviations will be a distance of (1.5)(0.6), or 0.9. And since standard deviation measures how far data is from the mean, your job is to determine which data points fall farther than 0.9 away from the mean of 2.95. That means that on the low end you're looking for values below:
Quote:
2.95 - 0.9 = 2.05

And on the high end you're looking for values above:
Quote:
2.95 + 0.9 = 3.85.

On the high side, only 3.9 and 4.0 are greater than 3.85, and on the low side only 1.9 and 1.8 are less than 2.05.

Therefore there are four such values that fit the criteria, so the correct answer is E.

Quote:
Most common mistake that happens in this question, when the test taker forgets to account for the 1.5 standard deviation i.e.to determine which data points fall farther than 0.9 away from the mean of 2.95
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Bunuel

The table above shows the GPA of 20 students last semester. If the average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6, how many of the grades are more than 1.5 standard deviations away from the mean?

A. None
B. 1
C. 2
D. 3
E. 4


Attachment:
GradeTable.png

1.5 standard deviations is 1.5 x 0.6 = 0.9.

So 1.5 standard deviations above the mean is 2.95 + 0.9 = 3.85, and 1.5 standard deviations below the mean is 2.95 - 0.9 = 2.05.

Looking at the chart, we see that 4 grades (1.8, 4.0, 1.9 and 3.9) are more than 1.5 standard deviations away from the mean.

Answer: E
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