Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 1.23 and 3.81?

Answer 1

The emperical rule or the 68-95-99.7 rule states that

(1) About 68% of the values fall within 1 standard deviation of the mean i.e from

Therefore 34% lies to the left i.e from to - 1 and 34% to the right i.e from to + 1

(2) About 95% of the values fall within 2 standard deviation of the mean i.e from

Therefore 47.5% lies to the left i.e from to - 2 and 47.5% to the right i.e from to + 2

(3) About 99.7% of the values fall within 3 standard deviation of the mean i.e from

Therefore 49.85% lies to the left i.e from to - 3 and 49.85% to the right i.e from to + 3

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Here we have the Mean () = 2.52 and = 0.43.

The value of 1.23 is below the mean. Therefore the number of standard deviations = (2.52 - 1.23)0.43 = 3

The value of 3.81 is above the mean. Therefore the number of standard deviations = (3.81 - 2.52)0.43 = 3

Therefore we need the % of values that lies between till = 99.7%