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Closing prices for a certain stock were recorded each day for a week

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Closing prices for a certain stock were recorded each day for a week  [#permalink]

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New post 16 Aug 2016, 06:10
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Question Stats:

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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

Attachment:
2016-08-16_1709.png
2016-08-16_1709.png [ 11.51 KiB | Viewed 2164 times ]

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Re: Closing prices for a certain stock were recorded each day for a week  [#permalink]

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New post 16 Aug 2016, 06:59
Bunuel wrote:
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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


The range that's 2 SD away would be 18.43 - 2*0.27 = 17.89 to 18.43 + 2*0.27=18.97
Only 2 days (Thursday and Friday), stocks are out of range.
Answer is 3 C)
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Re: Closing prices for a certain stock were recorded each day for a week  [#permalink]

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New post 16 Aug 2016, 07:26
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Top Contributor
Bunuel wrote:
Image
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

Attachment:
2016-08-16_1709.png


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:

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Re: Closing prices for a certain stock were recorded each day for a week  [#permalink]

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New post 06 Sep 2017, 23:57
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Re: Closing prices for a certain stock were recorded each day for a week   [#permalink] 06 Sep 2017, 23:57
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