Answer:
95% of the students have grade point averages that are between 1.76 and 3.28
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 2.52
Standard deviation = 0.38
Using the empirical rule, what percentage of the students have grade point averages that are between 1.76 and 3.28
1.76 = 2.52 - 2*0.38
So 1.76 is two standard deviations below the mean.
3.28 = 2.52 + 2*0.38
So 3.28 is two standard deviations above the mean
By the Empirical rule, 95% of the students have grade point averages that are between 1.76 and 3.28
