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A and B are graphical representations of normally distribute

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A and B are graphical representations of normally distribute [#permalink] New post 30 Jul 2018, 09:06
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#GREpracticequestion A and B are graphical representations of normally.PNG
#GREpracticequestion A and B are graphical representations of normally.PNG [ 79.62 KiB | Viewed 1544 times ]


A and B are graphical representations of normally distributed random variables X and Y, respectively, with relative positions, shapes, and sizes as shown. Which of the following must be true?

Indicate all such statements.

A. Y has a greater standard deviation than X.
B. The probability that Y falls within 2 standard deviations of its mean is greater than the probability that X falls within 2 standard deviations of its mean.
C. Y has a greater mean than X.
[Reveal] Spoiler: OA

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Re: A and B are graphical representations of normally distribute [#permalink] New post 23 Aug 2018, 09:22
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The dataset in B is more flat than A so S.D of B> S.D of A
Probability range for all SD in a normal distribution is fixed at 34%, 14% and 2% above and below the mean for 1st, 2nd and 3rd SD
The value directly beneath the protruded part of the curve is the mean. Clearly from the two graphs mean of y>mean of x

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Re: A and B are graphical representations of normally distribute [#permalink] New post 13 Jun 2019, 07:51
amorphous wrote:
The dataset in B is more flat than A so S.D of B> S.D of A
Probability range for all SD in a normal distribution is fixed at 34%, 14% and 2% above and below the mean for 1st, 2nd and 3rd SD
The value directly beneath the protruded part of the curve is the mean. Clearly from the two graphs mean of y>mean of x

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------------------------------
Need little more explication of the option C:
Flatter graph has highly dispersed data while the narrower one is not- meaning most of its values are centred around the mean.If the values has low dispersion, then they must have a mean closer to centralised values. But the highly dispersed values pull down the mean (?),therefore small mean.
Is the above correct ?
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Re: A and B are graphical representations of normally distribute [#permalink] New post 20 Jun 2019, 19:06
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Any explanations for why option C is correct?
Do we consider the X-axis value of the protruded parts in A and B curves? If yes, then C is true.

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Re: A and B are graphical representations of normally distribute [#permalink] New post 21 Jun 2019, 18:17
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The mean of a normal curve is the point along the horizontal axis below the “peak” of the curve. Red and blue lines, respectively

B is to the right of the highest point of curve A, so the mean of Y is larger than the mean of X.

Ask for further assistance.

Attachment:
#GREpracticequestion A and B are graphical representations of normally.PNG
#GREpracticequestion A and B are graphical representations of normally.PNG [ 77.73 KiB | Viewed 1536 times ]


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Re: A and B are graphical representations of normally distribute [#permalink] New post 16 Oct 2019, 01:28
Carcass wrote:
The mean of a normal curve is the point along the horizontal axis below the “peak” of the curve. Red and blue lines, respectively

B is to the right of the highest point of curve A, so the mean of Y is larger than the mean of X.

Ask for further assistance.

Attachment:
#GREpracticequestion A and B are graphical representations of normally.PNG


Regards


do not get it, please elaborate again
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Re: A and B are graphical representations of normally distribute   [#permalink] 16 Oct 2019, 01:28
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