Mrs. Smith's Algebra 2 class scored very well on the last quiz. With one exception, everyone
received an A. Within how many standard deviations of the mean do all the quiz grades fall?
97, 95, 97, 94, 93, 99, 91, 96, 94, 88, 92, 91
(1 point)
4
3
1
2
The mean of the quiz grades is (97+95+97+94+93+99+91+96+94+88+92+91) / 12 = 94.5
The standard deviation is the square root of the sum of the squared differences between each grade and the mean, divided by the number of grades.
Calculating the standard deviation we get:
((97-94.5)^2 + (95-94.5)^2 + (97-94.5)^2 + (94-94.5)^2 + (93-94.5)^2 + (99-94.5)^2 + (91-94.5)^2 + (96-94.5)^2 + (94-94.5)^2 + (88-94.5)^2 + (92-94.5)^2 + (91-94.5)^2) / 12 = 7.8
Since all the grades fall within 2 standard deviations of the mean, the answer is 2.