Question

In a normal distribution, 51 is the score that is two standard deviations above the mean, and 36 is the score one standard deviation below the mean. Find the mean

Answer 1

The mean is 41

Explanation:

Here , we are interested in finding the mean.

Firstly, let the standard deviation be x and the mean be y.

We are told that 51 is 2 standard deviations above the mean. What this mean is that if we subtract 2 standard deviations from 51, we will arrive at the mean.

Mathematically;

51 - 2(x) = y

y + 2x = 51 •••••••••(i)

We are also told that 36 is one standard deviation below the mean. What this mean is that if we subtract one standard deviation from the mean, we will have 36

Mathematically, that would be;

y-36 = x •••••••(ii)

Substitute ii into i directly;

We have

y + 2(y-36) = 51

y + 2y -72 = 51

3y -72 = 51

3y = 51 + 72

3y = 123

y = 123/3

y = 41