distribution and deviation

Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.45. Using the empirical rule, what percentage of the students have grade point averages that are at least 2.16 ?

Answer 1

mean = 2.61

SD = .45

what percentage is over 2.16? 84%

2.61 - 2.16 = 0.45 = one standard deviation below the mean

the empirical rule is 68 - 95 - 99.7

where 68 % of the data falls within one SD of the mean, with 32% outside and 16% on either side

95% falls within 2 SD of the mean. 99.7% falls within 3 SD of the mean.

so 100-16 = 84% are at least 2.16

It might help to draw a rough graph of a bell shaped curve

68% is in the middle. 32% outside. 32/2 = 16% on either side. 100-16 = 84% above 2.16