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03 Apr 2019, 02:56
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D
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Difficulty:
35%
(medium)
Question Stats:
73% (01:22) correct
27%
(01:35)
wrong
based on 390
sessions
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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%
eswarchethu135
GMAT 2: 640 Q49 V27
Posts: 276
03 Apr 2019, 03:46
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Attachment:
2019-04-03_6-43-52.png [ 7.89 KiB | Viewed 6273 times ]
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
General Discussion
07 Apr 2019, 06:14
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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
