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The age of a group of people follows a distribution, which is

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The age of a group of people follows a distribution, which is  [#permalink]

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New post 03 Apr 2019, 02:56
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The age of a group of people follows a distribution, which is symmetric about the average (mean) A. If 95% of the distribution falls within two standard deviation (SD) of the mean, then what percentage of the same distribution is less than A + 2SD?

    A. 68%
    B. 84%
    C. 95%
    D. 97.5%
    E. 99%

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Re: The age of a group of people follows a distribution, which is  [#permalink]

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New post 03 Apr 2019, 03:46
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As the distribution is symmetric, 2.5% lies below A-2SD and 2.5% lies after A+2SD as shown in the fig above.

So the percentage of the same distribution less than A + 2SD is 95% + 2.5% = 97.5%

OPTION: D
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Re: The age of a group of people follows a distribution, which is  [#permalink]

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New post 07 Apr 2019, 06:14

Solution


Given:
In this question, we are given that
    • The age of a group of people follows a distribution, which is symmetric about the average (mean) A.
    • 95% of the distribution falls within two standard deviation (SD) of the mean.

To find:
We need to determine
    • The percentage of the same distribution, which is less than A + 2SD.

Approach and Working:
As it is given that 95% of the distribution falls within two standard deviation (SD) of the mean, we can conclude that 5% lies outside this given range.

Now, as the distribution is symmetric about the mean A, we can also say that
    • Half of 5% or 2.5% lies to the right of A + 2SD
    • Therefore, the remaining (100 – 2.5) = 97.5% lies to the left of A + 2SD, or less than A + 2SD.

Hence, the correct answer is option D.

Answer: D

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Re: The age of a group of people follows a distribution, which is   [#permalink] 07 Apr 2019, 06:14
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