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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%
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The age of a group of people follows a distribution, which is symmetri...
We need to determine
•    The percentage of the same distribution, which is less than A + 2SD.
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.
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The age of a group of people follows a distribution, which is symmetri...
Understanding the Distribution
The age distribution of the group is symmetric about the mean A, indicating that the data is evenly spread around this central point.
Characteristics of the Distribution
- Symmetric Distribution: The left and right sides of the distribution are mirror images.
- Mean (A): The average age of the group.
- Standard Deviation (SD): A measure of the dispersion of ages from the mean.
Application of Standard Deviations
- Two Standard Deviations: In this context, 95% of the ages fall within A - 2SD and A + 2SD.
- Key Insight: Since the distribution is symmetric, the data can be divided equally around the mean.
Calculating the Percentage
- Less than A + 2SD: To find the percentage of the population that is younger than A + 2SD:
- Since 95% of the data is between A - 2SD and A + 2SD, it implies:
- 47.5% lies between A and A + 2SD (the upper half of the 95% interval).
- 50% is below the mean A.
- Therefore, the total percentage that is younger than A + 2SD is:
- 50% (below A) + 47.5% (between A and A + 2SD) = 97.5%.
Conclusion
Thus, the percentage of the distribution that is less than A + 2SD is 97.5%, making option 'D' the correct answer.
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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%Correct answer is option 'D'. Can you explain this answer?
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