Hi,  

A distribution has a standard deviation of   12.

 Find the z-score for each of the following locations in the distribution.

yes: z= (data point- mean)/standard deviation.

 a. Above the mean by 3 points.  z =  3/12 = 1/4

 b. Above the mean by 12 points. z = 12/12  = 1

 c. Below the mean by 24 points. z = -24/12 = -2

 d. Below the mean by 18 points. z = -18/12 = -3/2

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 (x-value = the mean) 50% of the area under the curve is to the left and %50 to the right



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.5%

and three standard deviations from the mean account for about 99.7%.

 

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