Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.51 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are no more than 2.07? Please do not round your answer.

Answer 1

15.87%

Explanation:

Given that :

Mean (m) = 2.51

Standard deviation (σ) = 0.44

Percentage of students with grade point average no more than 2.07

Using the relation :

Zscore = (X - mean) / standard deviation

X = 2.07

Zscore = (2.07 - 2.51) / 0.44

Zscore = - 0.44 / 0.44

Zscore =. - 1

P(Z < - 1) : using the z table

P(Z < 1) = 0.1587

Hence, Percentage of students with grade point average no more than 2.07 is (0.1587 * 100%) = 15.87%