The following statement in your reasoning:

**Quote:**

Within one standard deviation would be between 35 and 45, since the standard deviation is 10.

is NOT correct.

So let's concentrate on what the phrase

**Quote:**

68 percent of all values lie within one standard deviation of the mean

means.

The structure of this phrase is:

*some set of values* **lie within** *x* of

*y*.

EXAMPLE: "Half of all values lie within 5 units of 10". It sets up the range [10 – 5, 10 + 5]. So this half of the values lie in the range [5, 15] (which means between 5 and 15).

In other words, phrase "lie within 5 units of 10" means "no farther than 5 units from 10" and it defines the range [5, 15], which is 5 × 2 = 10 units wide.

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Also NOTE, that reasoning

**Quote:**

therefore between 50 and 60 are in the 5%

could NOT be made based on the fact that 95 percent of the values lied within two standard deviations of the mean, even if the area within two standard deviations was from 30 to 50.

That fact, 95 percent of the values lie within two standard deviations of the mean, would have implemented that 5% lie outside the range [30, 50]. That range is NOT limited by 60 or any other number. So there would have been less than 2,5% of the values, which had lied from 50 to 60.