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The table above shows the GPA of 20 students last semester.

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by swerve » Mon Jan 28, 2019 7:43 am

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E

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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

The OA is E

Source: Veritas Prep
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by Brent@GMATPrepNow » Mon Jan 28, 2019 8:34 am
swerve wrote:Image

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
---------------ASIDE--------------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc


So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
----ONTO THE QUESTION!!!------------------------

The average (arithmetic mean) of the 20 GPAs is 2.95 and the standard deviation is 0.6
1.5 standard deviations ABOVE the mean = 2.95 + 1.5(0.6) = 3.85
1.5 standard deviations BELOW the mean = 2.95 - 1.5(0.6) = 2.05

How many of the grades are MORE THAN 1.5 standard deviations away from the mean?
So, we're looking for grades that are EITHER less than 2.05 OR greater than 3.85

Check the values....
Image

There are 4 such values.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Mon Jan 28, 2019 9:31 am
swerve wrote:Image

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
Source: Veritas Prep
$$\left( {\mu \,;\,\sigma } \right) = \left( {2.95\,;\,0.6} \right)$$
$$?\,\,\,:\,\,\,\left| {{\text{grade}} - \mu } \right| > 1.5\sigma \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{\text{grade}}\,\, < \,\,\mu - 1.5\sigma \,\, = \,\,2.05\,\,\,\,\underline {{\text{or}}} \,\,\,\,{\text{grade}} > \mu + 1.5\sigma = 3.85$$
$${\text{?}}\,\,{\text{ = }}\,\,4\,\,{\text{cases}}\,\,\,\left( {{\text{by}}\,\,{\text{inspection}}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Wed Jan 30, 2019 6:01 pm
swerve wrote:Image

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

The OA is E

Source: Veritas Prep
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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