Regardless of the actual values of the mean and the standard deviation, any sample that is 2 standard deviations above the mean is placed on (about) the 95th percentile.

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This is a true(O) or false(X) question I had to answer and then explain on it but I got the answer wrong from what the solution shows can you look at the question and answer that I had and then the correct solution and point out what I did wrong and then explain how to solve it.

The question and answer that I had: 

  1. Regardless of the actual values of the mean and the standard deviation, any sample that is 2 standard deviations above the mean is placed on (about) the 95th percentile.

Answer: (O)    whole data lie within three standard deviations of mean .

                 rule is  68-95-99.7

                 Which means 68% data lie within one standard deviations

                  95% data lie within two standard deviations

                  99.7% data lie within three standard deviations

                  95% data lie within two standard deviations 

This was the correct solution:  [X] About 95% of the population are (normally) distributed within 2 standard deviations from the mean, leaving just half of it, or 2.5%, more than 2σ above the mean.

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