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Letter grades on a Statistics 101 test from a class consisting of 200 students are presented in the pie chart below:
a. How many students received a "D"?
b. If a "C" or better is required to take Statistics 102, how many students in this class will be eligible to take that course?
c. If 75% of those that received a "B" are international students, how many domestic students also got a "B"?
d. If the top 120 students are exempted from a bonus quiz, what is the minimum grade of those exempted?

Let's break down the information from the pie chart and address each part of the question.

We know the following from the pie chart for a class of 200 students:

- Grade A: 22%
- Grade B: 32%
- Grade C: 21%
- Grade D: 13%
- Grade F: 12%

**a. How many students received a "D"?**

The percentage of students who received a D is 13%. To find the number of students who received a "D", we calculate:

\[
\text{Number of students with a D} = 0.13 \times 200 = 26 \text{ students}.
\]

**b. If a "C" or better is required to take Statistics 102, how many students in this class will be eligible to take that course?**

Students eligible to take Statistics 102 are those with a grade of A, B, or C. We sum up the percentages of these students:

\[
A + B + C = 22\% + 32\% + 21\% = 75\%
\]

Now, we calculate how many students this corresponds to:

\[
\text{Eligible students} = 0.75 \times 200 = 150 \text{ students}.
\]

**c. If 75% of those that received a "B" are international students, how many domestic students also got a "B"?**

First, find the number of students who received a "B":

\[
\text{Number of students with a B} = 0.32 \times 200 = 64 \text{ students}.
\]

Next, find how many of these are international students:

\[
\text{International students with a B} = 0.75 \times 64 = 48 \text{ students}.
\]

So, the number of domestic students who received a "B" is:

\[
\text{Domestic students with a B} = 64 - 48 = 16 \text{ students}.
\]

**d. If the top 120 students are exempted from a bonus quiz, what is the minimum grade of those exempted?**

The top 120 students consist of those with the highest grades. Let's calculate the cumulative number of students starting from the highest grade:

- Students with an A: \( 0.22 \times 200 = 44 \)
- Students with a B: \( 0.32 \times 200 = 64 \)
- Students with a C: \( 0.21 \times 200 = 42 \)

Now, sum these:

- A + B: \( 44 + 64 = 108 \)
- Adding C grade students: \( 108 + 42 = 150 \)

So, to exempt the top 120 students, we include all students with an A and B (108 students), and 12 students with a C. Therefore, the minimum grade of those exempted is **C**.

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Let me know if you need more details or have any questions! Here are 5 related questions for further understanding:

1. What percentage of students received a grade lower than C?
2. How many students would need to improve by one grade to be eligible for Statistics 102?
3. What is the ratio of students who received an A to those who received a D?
4. If the passing grade is a D or higher, what percentage of students failed the exam?
5. If 10 more students were added to the class and all received an A, what would the new percentage of students with an A be?

**Tip:** When analyzing pie charts, always ensure that the total percentage adds up to 100% to avoid calculation errors!

Letter grades on a Statistics 101 test from a class consisting of 200 students are presented in the pie chart below: a. How many students received a 'D'? b. If a 'C' or better is required to take Statistics 102, how many students in this class will be eligible to take that course? c. If 75% of those that received a 'B' are international students, how many domestic students also got a 'B'? d. If the top 120 students are exempted from a bonus quiz, what is the minimum grade of those exempted?

Solve a Statistics 101 test letter grade distribution problem where 200 students received various grades. Calculate the number of students who received a 'D', determine eligibility for taking Statistics 102, and analyze international student distribution.

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