Question

Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall?
91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97

A. 1
B. 2
C. 4
D. 3

Answer 1

Answer: option B. 2

Explanation:

1) Find the mean:

mean = sum of the values / number of data

The number of data is 12, so:

mean = (91 + 92 + 94 + 88 + 96 + 99 + 91 + 93 + 94 + 97 + 95 + 97) / 12

mean = 1127 /12 = 93.917

2)  Find the variance:

variance = sum of squares of the differences between each data and the media, divided by thenumber of data - 1

variance = (106.97)/(12-1) = 106.97 / 11 = 9.720

3) Find the standard deviation

standard deviation = square root of variance = √(9.720) = 3.118

4) Find the difference of the maximum and the minimun grades with the media:

maximum grade: 99 - 93.917 = 5.083

Find how many standard deviations that is: 5.083 / 3.118 = 1.63

minimum grade: |88 - 93.917| = 5.917

Find how many standard deviations that is: 5.917 / 3.118 = 1.9

5) Conclusion: all the quiz grades falls inside 2 standard deviations form the mean.