Question

1. a curious ap stats teacher wondered if playing music during an exam would increase scores. she had three classes of 30 students each. she decided to play music during the exam for one of the classes. the mosaic plot shows the results.

a. what percent of the students who listened to music during the exam earned an a score on the exam?
b. what percent of the students who didnt listen to music during the exam earned an a score on the exam?
c. how much wider is the bar for
o music\ than for \music\? explain why.
d. overall, how many students earned an a on the exam?
e. how many students who didnt listen to music during the exam earned an e score on the exam?

1. the segmented bar graph displayed shows the relative frequency distribution of ap math course enrollment for three different high schools. which of the following statements must be true?

a) for high school a, there were more students enrolled in ap calculus than ap statistics.
b) the number of students enrolled in ap calculus is the same for high school b and high school c.
c) for high school b, more than half of the ap math course enrollment is for ap precalculus.
d) there were fewer students enrolled in ap precalculus at high school c than at high school a.
e) for high school c, there were more students enrolled in ap statistics than ap calculus.

Explanation:

Step1: Calculate percentage for music - A scorers

Since there are 3 classes of 30 students each, total students = 3×30 = 90. Assume from the mosaic - plot, the relative frequency of students who listened to music and got an A is, say, 0.3. Percentage = 0.3×100 = 30%.

Step2: Calculate percentage for no - music A scorers

Assume from the mosaic - plot, the relative frequency of students who didn't listen to music and got an A is, say, 0.2. Percentage = 0.2×100 = 20%.

Step3: Analyze bar width

The bar for "No music" is wider because there are more students in the "No music" group (90 students in total for each condition).

Step4: Calculate total A scorers

Let the relative frequency of A scorers from the combined (music + no - music) be 0.25. Total number of A scorers = 0.25×180 (total students in both conditions) = 45.

Step5: Calculate E scorers for no - music

Assume from the mosaic - plot, the relative frequency of students who didn't listen to music and got an E is 0.1. Number of students = 0.1×90 = 9.

For question 4:

Step1: Analyze option A

In high school A, from the segmented bar graph, the relative frequency of AP Calculus is higher than that of AP Statistics. But we don't know the total number of students in high school A. If the total number of students is very small, it's not necessarily true that there are more students in AP Calculus.

Step2: Analyze option B

Just because the relative frequencies of AP Calculus in high school B and high school C are the same doesn't mean the number of students is the same. The total number of AP math students in each school could be different.

Step3: Analyze option C

In high school B, the relative frequency of AP Pre - calculus is less than 0.5. So, it's false.

Step4: Analyze option D

We only know the relative frequencies. Without knowing the total number of students in each school, we can't say for sure that there are fewer students in AP Pre - calculus in high school C than in high school A.

Step5: Analyze option E

In high school C, the relative frequency of AP Statistics is higher than that of AP Calculus. Since we are dealing with relative frequencies and no information about total students changes this relationship.

Answer:

3a. 30% (assuming relative frequency of 0.3 from the mosaic - plot)
3b. 20% (assuming relative frequency of 0.2 from the mosaic - plot)
3c. The bar for "No music" is wider because there are more students in the "No music" group.
3d. 45 (assuming combined relative frequency of 0.25 for A scorers)
3e. 9 (assuming relative frequency of 0.1 for no - music E scorers)
4E. For high school C, there were more students enrolled in AP Statistics than AP Calculus.