A mean of 2.5 in the standard deviation of 0.38 using empirical rule what percentage of the students have a grade point average is that are between 1.36 and 3.64

Answer 1

The GPA's are within 3 standard deviations of the mean. The empirical rule, 68, 95, 99,7 means 99.7% of the students had GPA's between 1.36 and 3.64. or between 2.5 + and - 3 standard deviations.

2.5-1.36=1.14 1.14 divided by 038 = 3 standard deviations

3.64-2.5=1.14 again all within 3 standard deviations of the mean.

Sometimes, they just call the rule 68, 95, 99. But more precisely it's 99.7% of the grades fall within 3 standard deviations of the mean, nearly 100% if rounded off to nearest 1%.

68% fall within 1 standard deviation of the mean

95% fall within 2 standard deviations

99.7% fall within 3 standard deviations

That's the empirical rule