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The scores on a psychology exam were normally distributed with a mean of 67 and a standard deviation of 8.

If 500 students took the exam, approximately how many students scored below 75
 
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1 Answer

67 + 8 z = 75
 
z = 1
 
Looking at a z-score chart (see http://easycalculation.com/statistics/positive-z-score-chart.php) we find that 84.13% of the population is below z = 1.
 
So 84.13% * 500 = 84.13 * 5 = 84.13 * 10 / 2 = 841.3 / 2 = 420 students scored below 75%.