Under what circumstances is a score that is located 5 points

Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?

a.

When the population mean is much less than 5

b.

When the population mean is much greater than 5

c.

When the population standard deviation is much less than 5

d.

When the population standard deviation is much greater than 5

Solution

As the relative position of the mean is the z score, we look at the formula for the z score.

As

z = (x - u) / sigma

and x - u = 5 (fixed),

then increasing sigma (standard deviation) will make the z score low.

Thus, the answer is OPTION D: When the population standard deviation is much greater than 5. [answer]