To find the standard deviation, first find the mean of the quiz grades:
(97 + 95 + 97 + 94 + 93 + 99 + 91 + 96 + 94 + 88 + 92 + 91) / 12 = 93.75
Next, find the variance by squaring the differences between each score and the mean, then averaging them:
((97-93.75)^2 + (95-93.75)^2 + (97-93.75)^2 + (94-93.75)^2 + (93-93.75)^2 + (99-93.75)^2 + (91-93.75)^2 + (96-93.75)^2 + (94-93.75)^2 + (88-93.75)^2 + (92-93.75)^2 + (91-93.75)^2) / 12 ≈ 9.97
Then, take the square root of the variance to find the standard deviation:
√9.97 ≈ 3.16
Therefore, all the quiz grades fall within approximately 3 standard deviations of the mean. So the correct answer is 3.
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
Responses
show all your work
3
3 - not selected, this is the correct answer
1
1 - no response given
2
2 - incorrect
4
1 answer