Question

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.4.

Using the empirical rule, what percentage of the students have grade point averages that are at least 1.82? Please do not round your answer.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the percentage of students with GPAs at least 1.82, we first need to find the z-score of 1.82.

Z = (X - μ) / σ
Z = (1.82 - 2.62) / 0.4
Z = -0.8 / 0.4
Z = -2

Now, we can use the empirical rule to find the percentage of students with a z-score less than -2. According to the empirical rule:
- Approximately 2.5% of the data falls more than 2 standard deviations below the mean.

Therefore, approximately 2.5% of students have a GPA of at least 1.82.