Mrs. Jones Algebra 2 class scored very well on yesterday’s quiz. With one exception, everyone received an A. Within how many standard deviations of the mean do all the quiz grades fall?
91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
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Step 1: Find the mean of the quiz grades
Mean = (91 + 92 + 94 + 88 + 96 + 99 + 91 + 93 + 94 + 97 + 95 + 97) / 12
Mean = 1153 / 12
Mean = 96.08 (rounded to 2 decimal places)
Step 2: Find the standard deviation of the quiz grades
Using a calculator or software, we can find the standard deviation to be 3.58 (rounded to 2 decimal places)
Step 3: Calculate the range of grades that fall within one standard deviation of the mean
96.08 + 3.58 = 99.66
96.08 - 3.58 = 92.50
Therefore, all the quiz grades fall within one standard deviation of the mean, which is between 92.50 and 99.66.