Mrs. Smiths 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
A)2
B)1
C)3
D)4
B) 1
First, find the mean of the quiz grades:
(97+95+97+94+93+99+91+96+94+88+92+91) / 12 = 94.5
Next, find the standard deviation:
1. Calculate the variance:
(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 = 8.75
2. Take the square root of the variance to find the standard deviation:
√8.75 ≈ 2.96
Since all the quiz grades fall within 1 standard deviation of the mean (94.5 +/- 2.96), the answer is B) 1.