question in description

Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.55 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are less than 3.72? Please do not round your answer.

Answer 1

z=(3.72-2.55)/.39=1.17/.39=3

the empirical rule says 99.7% fall within 3 standard deviations from the mean

but you also want to add in the left tail =(1-.997)/2 =.003/2= .0015

so .997+.0015= .9985 = 99.85% have less than 3.72 gpa

that's not rounded off, although the empirical rule itself is an approximation, a very close approximation which does some rounding.

to get a closer approximation, use z tables or a statistics calculator. It should give you 99.865%