in a standard normal distributuion, above which z-score do approximately 57% of the data lie?

Question

in a standard normal distribution, above which z-score do approximately 57% of the data lie?

Answer 1

The z-score table tells you, for each value, how much of the data lies behind that point. So if we're looking for a value which 57% is above, we are really looking to find the value for which 43% is behind, meaning the z-score is .43. So, we need to find the z-score which gets you .43.

 

THE PROBLEM is that z-score table starts from .5, so where's .43?

 

Well, the reason why z-scores start from .5 is because it only deals with positive values of the normal distribution. Everything below .5 is a negative, so we know that .43 is somewhere in the "negative zone".

 

How can we find a value in the "negative zone"?

 

The relationship between negative and positive z-scores is as follows:

 

z(-a) = x

z(a) = 1- x

 

So, if we're looking for z-score (-A) which gets you .43, we are looking for the z-score (A) which gets you 1-.43 =.57

 

Find the z-score which gets you .57, make it a negative, and, boom, there's our z-score for .43.

 

Let's try it:

 

z(.18) = .57

 

therefore,

 

z(-.18) = .43

 

The z-score is -.18.

 

Look over a graph of the normal distribution and this idea will become more clear. Remember, the z-score chart only kicks in half way through, at the center of the graph.