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 0.38. Using the empirical rule, what percentage of the students have grade point averages that are between 1.76 and 3.28

Answer 1

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