A normal distribution has a mean of 60 and a standard deviation of 2. Determine the z- score for the data value of 22.

z score is -19

Work Shown:

x = 22 is the raw score

mu = 60 is the mean

sigma = 2 is the standard deviation

z = (x-mu)/sigma = formula to find z scores

z = (22 - 60)/2

z = -38/2

z = -19

The z score of -19 means we are 19 standard deviations below the mean. Anything beyond 3 standard deviations is often considered unusual/rare as most of the data in the normal distribution is within 3 standard deviations (approximately 99.7% of the distribution)