Question

If a distribution has a mean of 100 and a standard deviation of 15, what value would be +2 standard deviations from the mean?

Answer 1

The value that is `+2` standard deviations from the mean is `130`.

Explanation:

For such an exercise, we use `Z`-score, which means whether the value is below or above mean (shown by positive or negative sign) and by how much (times the standard deviation.

This is calculated as `value=mu+zxxsigma`, where `mu` is mean, `sigma` is standard deviation and `z` is `z`-score assuming that the distribution is normal.

In the given case, what is desired is the value that would be `+2` standard deviations from the mean i.e. `z`-score is `+2`. Here `mu=100` and `sigma=15`.

Hence, the value that would be `+2` standard deviations from the mean is

`100+2xx15=130`.