In a normal distriution above which z score do approximately 63 percent of the data lie?

Question

At first I was thinking 1.79

Answer 1

Lallyah,

 

In any probability distribution function, the total area underneath the distribution from -∞ to +∞ must be 1.

 

The Normal or Gaussian distribution function is symmetrical about a z value of 0, so half its probability is below zero and half above zero.  

 

BTW, the reason you calculate a z-value is it transforms your Normal distribution value to the corresponding value in a standardized Normal curve whose mean is zero and standard deviation is 1.  Then you can look up the computed area in one standardized table in a book or on a website.  This table computes the area from z=0 because of the symmetry of the Normal distribution so you have to piece your answer together.

 

Since you want to know the z value whereby 63% of the probability or area is above or to the right of that z-value, you know that the z-value must be negative since 50% is to the right of z=0.

 

Now 63% = 50% + 13%.  So look up the z-value for 13% and then make its sign negative.

Hence, z = - 0.332.

 

Finally, you can transform this z-value back to your starting non-standard Normal with its mean and standard deviation values.

 

 

Answer 2

Get a z-score table:

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

 

If 63% lie above the z-score, then 37% lie below, or to the left.

On the "negative" chart locate the value closest to 0.37. It is 0.3070 that corresponds to the z-score of -0.33.