In a set of 85 ACT scores where the mean is 22 and the stand

In a set of 85 ACT scores, where the mean is 22 and the standard deviation is 5.39, how many scores are expected to be lower than 16.61 (one standard deviation below the mean)? How many of the 85 scores are expected to be below 32.78 (two standard deviations above the mean)? Click the icon to view the graph of the Normal Distribution. How many scores are expected to be lower than 16.61? Scores (Round to the nearest integer as needed.) How many of the 85 scores are expected to be below 32.78? Scores (Round to the nearest integer as needed.)

Solution

a)

From the table, those lower than 1 standard deviation is 50% - 34.13% = 15.87%.

Thus, as 15.87% of 85 is 0.1587*85 = 13.4895 = 13 scores [ANSWER] are less than 16.61.

[ANSWER, 13]

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b)

From the figure, those below 2 standard deviations from the mean is 100% - 2.15% - 0.13% = 97.72%.

Thus, 97.72% of 85 is 0.9772*85 = 83.062 = 83 scores. [ANSWER, 83]