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.3
D.4
A. 1
To find the standard deviation, we first need to find the mean of the quiz grades.
Mean = (91 + 92 + 94 + 88 + 96 + 99 + 91 + 93 + 94 + 97 + 95 + 97) / 12 = 93.5
Next, we calculate the variance:
Variance = ((91-93.5)^2 + (92-93.5)^2 + (94-93.5)^2 + (88-93.5)^2 + (96-93.5)^2 + (99-93.5)^2 + (91-93.5)^2 + (93-93.5)^2 + (94-93.5)^2 + (97-93.5)^2 + (95-93.5)^2 + (97-93.5)^2) / 12
= (6.25 + 2.25 + 0.25 + 30.25 + 5.06 + 32.25 + 6.25 + 0.25 + 0.25 + 13.06 + 6.25 + 13.06) / 12
= 19.15
Now, we take the square root of the variance to get the standard deviation:
Standard Deviation = √19.15 ≈ 4.37
Since all the quiz grades fall within 1 standard deviation from the mean of 93.5, the correct answer is A. 1.