Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.612.61 and a standard deviation of 0.390.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.831.83 and 3.393.39?

Answer 1

Given that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.39

Now using the empirical rule we need to find what percentage of the students have grade point averages that are between 1.83 and 3.39

Empirical Rule

Now for a data with bell shaped distribution the empirical rule states that about 68% of the data falls within 1 standard deviation, about 95% of the data falls within 2 standard deviation and about 99.7% of the data falls within 3 standard deviation.

Coming back to our problem

Now using the empirical rule we need to find what percentage of the students have grade point averages that are between 1.83 and 3.39

Here,

Now we see that,

Now we need to find what percentage of the students have grade point averages that are between 1.83 and 3.39

[By the Empirical Rule]

Hence 95% of the students have grade point averages that are between 1.83 and 3.39