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Closing prices for a certain stock were
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20 Sep 2021, 08:56
20 Sep 2021, 08:56
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Question Stats:
81% (01:12) correct
18% (02:27) wrong based on 11 sessions
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Closing prices for a certain stock were recorded each day for a week in the table above. If the monthly average (arithmetic mean) was 18.43 and the standard deviation was 0.27, how many days during this week did the closing price fall within two standard deviations from the average?
A. 1
B. 2
C. 3
D. 4
E. 5
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Re: Closing prices for a certain stock were
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20 Sep 2021, 09:01
20 Sep 2021, 09:01
Carcass wrote:
Closing prices for a certain stock were recorded each day for a week in the table above. If the monthly average (arithmetic mean) was 18.43 and the standard deviation was 0.27, how many days during this week did the closing price fall within two standard deviations from the average?
A. 1
B. 2
C. 3
D. 4
E. 5
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.
-----------------------------
For this question, the mean is 18.43 and the standard deviation is 0.27
So, two standard deviations = (2)(0.27) = 0.54
So, two standard deviations BELOW the mean = 18.43 - 0.54 = 17.89
And two standard deviations ABOVE the mean = 18.43 + 0.54 = 18.97
So, the RANGE of acceptable values lies between 17.89 and 18.97
When we check the table, we see there are 3 values in this range
Answer: C
gmatclubot
Re: Closing prices for a certain stock were [#permalink]
20 Sep 2021, 09:01
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