sanman wrote:

Hi,

I thought that a SD of 2.5 from a MEAN of 20 would be a value dispersed 2.5 units away from 20, So I subtracted 2.5 from 20 and got the answer wrong.

Can you please explain why did we multiply SD with 2.5?

Cheers

There are two different things here:

SD is 3.

We need to find values which are 2.5 SD away from the mean.

When we say that a value is at mean, it is 20.

When we say that a value is 1 SD away from mean, it means the value is 3 away from mean (because 1 SD is 3). So it can be either 17 or 23.

When we say that a value is 2 SD away from mean, it means that the value is 2*3 away from mean (because 2 SD is 6). So it can be either 14 or 26.

When we say that a value is 2.5 SD away from mean, it means that the value is 2.5*3 away from mean. So it can be either 12.5 or 27.5.

Since we want a value which is more than 2.5 SD away, the value must be less than 12.5 or greater than 27.5.

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