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# The standard deviation of a normal distribution of data is 2

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The standard deviation of a normal distribution of data is 2 [#permalink]

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16 Aug 2010, 11:15
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The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 43. What is a possible value for the mean of the distribution?

A. 46
B. 47
C. 48
D. 49
E. 50
[Reveal] Spoiler: OA

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16 Aug 2010, 11:21
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aiming4mba wrote:
The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 43. What is a possible value for the mean of the distribution?

a.46
b.47
c.48
d.49
e.50

The standard deviation ({SD}) = 2;

3 standard deviations below the mean is greater than 43:

{Mean} - 3*{SD} > 43;
{Mean} - 6 > 43;
{Mean} > 49.

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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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29 May 2015, 02:10
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Hi All,

Presenting the visual representation of the normal distribution curve:

A normal distribution curve is also known as the bell curve.

Such questions on standard deviation are centered around the following 4 variables:

I. Mean of the distribution
II. Standard Deviation of the distribution
III. A data point of the distribution
IV. Distance of data point from the mean

These variables are related as

Data Point = Mean +/- Distance from the mean where the distance from mean is expressed in terms of standard deviation

Out of these 4 variables, the question is likely to give you 3 and ask you to find the fourth variable.

Let's see what have we been given in the question statement

I. Mean- Need to find (let's assume it to be $$m$$)
II. Standard deviation of the distribution - $$2$$
III. A data point of the distribution- $$43$$
IV. Distance of data point from the mean - $$3$$ standard deviations below mean

We can write

$$43 < m - 3 * 2$$ ( we put in a '-' sign as the data point is below mean)

$$m > 49$$. Out of the given options only Option E has a value greater than $$49$$.

Hope this helps

Regards
Harsh
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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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27 Sep 2013, 04:25
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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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04 May 2014, 03:29
Hello Bunuel,
Could you mind explaining what "2 (or 3) deviation below/above mean' means? I could apply formula to solve such question but I don't really understand the nature of the problem?

Thank you indeed,

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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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04 May 2014, 08:39
yenh wrote:
Hello Bunuel,
Could you mind explaining what "2 (or 3) deviation below/above mean' means? I could apply formula to solve such question but I don't really understand the nature of the problem?

Thank you indeed,

The standard deviation of a set is some number as well as the mean. We are told that 3 standard deviations below the mean is greater than 43. 3 standard deviations below the mean is {Mean} - 3*{SD}, which we are told that is greater than 43.

Hope that similar questions given here will help to understand better.
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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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12 Jun 2016, 11:51
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yenh wrote:
Hello Bunuel,
Could you mind explaining what "2 (or 3) deviation below/above mean' means? I could apply formula to solve such question but I don't really understand the nature of the problem?

Thank you indeed,

Here's a video lesson on this topic:

Here's a practice question for reinforcement:

Cheers,
Brent
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Re: The standard deviation of a normal distribution of data is 2 [#permalink]

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18 Nov 2017, 00:50
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Re: The standard deviation of a normal distribution of data is 2   [#permalink] 18 Nov 2017, 00:50
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