Area Under a Portion of the Normal Curve (2 of 4)

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Suppose you wanted to know the proportion of students receiving scores between 70 and 80. The approach is to figure out the proportion of students scoring below 80 and the proportion below 70. The difference between the two proportions is the proportion scoring between 70 and 80. First, the calculation of the proportion below 80. Since 80 is 20 points above the mean and the standard deviation is 10, 80 is 2 standard deviations above the mean.

z equals x minus mu over sigma = (80 - 60)/10 = 2

A z table can be used to determine that .9772 of the scores are below a score 2 standard deviations above the mean.

normal distribution showing proportion above 2
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