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How many maple trees had a diameter greater than 49.4 cm ?

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Carcass
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How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   17 May 2021, 14:02
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How many maple trees had a diameter greater than 49.4 cm ?

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How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   19 May 2021, 12:46
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Carcass wrote:
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How many maple trees had a diameter greater than 49.4 cm ?

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Normal Distribution = X̄ ± xσ
where,
X̄ = Mean
σ = standard deviation (SD)
x = number of deviation ranging from 0 to 3

Here, 49.4 is 1 standard deviation (SD) above mean
i.e. 49.4 = 42 + 1(7.4)

We know, 1 SD above mean represents 84 percent of the data
Therefore, 16% of all Maple trees will have diameter above 49.4 i.e. \frac{16}{100}(50) = 8
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Re: How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   21 May 2021, 02:03
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We know standard deviation curve has divided into 34%,14%, and 2% both in left and right with increment in each unit above or below the standard deviation. Here average is provided 42 and adding one unit above S.D. is 49.4 and left with (14+2)%. hence ans is 16% of 50=8.
hope it helps.
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Re: How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   20 Aug 2021, 22:38
why did you consider it as normal distribution?
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Re: How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   21 Aug 2021, 06:49
greenmonomer wrote:
why did you consider it as normal distribution?


Because that is the only Distribution asked by ETS in GRE
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How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   21 Aug 2021, 08:07
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Actually when data is skewed, interquartile range and median are better parameters of descriptive stats than mean and variation. IMO, this question is missing a point about normal distribution. Hence, the assumption about normal distribution is the only way to solve it. Otherwise, there is no way to establish a link between mean and standard deviation. For normal distribution though, when we divide the difference between a mean and any variable by a standard deviation we get the standard normal distribution with mean=0 and standard deviation=1
KarunMendiratta wrote:
greenmonomer wrote:
why did you consider it as normal distribution?


Because that is the only Distribution asked by ETS in GRE
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Re: How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   14 Sep 2021, 07:00
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KarunMendiratta wrote:
greenmonomer wrote:
why did you consider it as normal distribution?


Because that is the only Distribution asked by ETS in GRE


True, but if this were a QC question, we'd couldn't assume a normal distribution.
On test day, if we're not told a distribution is normal, we can't assume it to be so.
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Re: How many maple trees had a diameter greater than 49.4 cm ? [#permalink] New post   21 Sep 2022, 01:58
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