Finding standard deviation above a mean?

Question

How do I find the amount that represents 1.96 standard deviations above the mean if the mean is 36.74?

Answer 1

In a normal distribution, the z-score for a given data value, x, is z = (x - μ) / σ, where μ is the mean and ο is the standard deviation. If z is positive, then x lies z units above the mean and if z is negative, then x lies lzl units below the mean.

Since z = 1.96, μ = 36.74, and σ = 20.19 (given in your comment), we have:

1.96 = (x - 36.74) / 20.19

Solving for x, we get x = 76.3. So, 76.3 lies 1.96 standard deviations above the mean.