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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%.
