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 Post subject: GRE Statistics (Select One)
PostPosted: Sat May 12, 2012 11:32 am 
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Posts: 424
The distribution of seed pod diameters of a particular tree is normal (bell-curve-shaped), with a mean of 3 inches and a standard deviation of 0.25 inches. Which is the closest proportion of seed pods that have a diameter between 2.75 inches and 3.25 inches?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

The correct answer is (D). The values 2.75 and 3.25 were obtained by subtracting one standard deviation from the mean of 3 to get 2.75 inches, and adding one standard deviation to it to get 3.25. A normal distribution has about 68 % of its data within one standard deviation of the mean. Of the answer choices, 2/3 is the closest value to 68%, and thus the answer is D.
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This answer is not at all clear. Could you explain it better, please?

I will really appreciate it.


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 Post subject: Re: t.1, s.2, qt.17: statistics, normal distribution.
PostPosted: Sun May 13, 2012 3:13 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
First of all note:
68% is 0.68
2/3 is 0.66… ≈ 0.67

Secondly, you should review the facts about normal distribution.

This is the fact we use here:
A normal distribution has about 68% of its data within one standard deviation of the mean.

Here is the diagram, which shows how the mean (3.00 inches) and the values 2.75 inch, 3.25 inch relate according to the 68%-rule.

Image

Each point represents the number of seed pods of a certain diameter.

The mean value is:
(diameter1 × number1 + diameter2 × number2 + … + diameterN × numberN) / (number1 + number2 + … + numberN)

The grey points represent all seed pods that have their diameters between 2.75 and 3.25. There are (numberK + … + numberM) of those seed pods.

The theorem says that (numberK + … + numberM)/(number1 + … + numberN) is about 68%.


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 Post subject: Re: GRE Statistics (Select One)
PostPosted: Tue Aug 20, 2013 8:36 am 
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Hi ,

The answer is clear to me but for further understanding I have a question.How can be represent standard deviation on the graph of normal distribution?


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 Post subject: Re: GRE Statistics (Select One)
PostPosted: Thu Aug 22, 2013 3:08 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
hgablid wrote:
The answer is clear to me but for further understanding I have a question. How can be represent standard deviation on the graph of normal distribution?
Standard Deviation is a number. It is one particular value, a parameter (characteristic) of a distribution. The less it is, the more data tend to the mean.

Of course, there is no point in plotting that particular number on the graph, however, in case of the normal distribution, we can plot what it represents.

We know that about 68% of the data lie within one standard deviation of the mean, 95% – within two, 99.7% – within three. So we can show these areas on the graph, where 68%, 95%, 99.7% of the data lie.

Image

About 34% of the seed pods are within one standard deviation on the either side of the mean (together they make 34% + 34% = 68%). Another bars to the left and right will bring us additional 13.5% of the seed pods each (13.5% + 34% + 34% + 13.5% = 95%) and so on.

In other words, we can say that about 68% of the seed pods are between 2.75 and 3.25 inches in diameter. Similarly with 95%, 99.7%.


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