Question

Question was provided via image upload.

Explanation:

Part B

Step1: Identify cumulative frequencies

From the histogram, cumulative frequency for 45 - 48 is 9, and for 45 - 49 is 14.

Step2: Calculate frequency for 49

To find the number of people who answered 49 correctly, subtract the cumulative frequency of the previous interval (45 - 48) from the cumulative frequency of 45 - 49. So, \(14 - 9 = 5\)? Wait, no, wait. Wait, the intervals: 45, 45 - 46 (4), 45 - 47 (8), 45 - 48 (9), 45 - 49 (14), 45 - 50 (20). Wait, no, the x - axis labels: 45, 45 - 46, 45 - 47, 45 - 48, 45 - 49, 45 - 50. The cumulative frequencies: at 45, it's 2? Wait, no, the first bar is up to 2 (for 45), then 4 (45 - 46), 8 (45 - 47), 9 (45 - 48), 14 (45 - 49), 20 (45 - 50). Wait, no, the cumulative frequency for 45 - 49 is 14, and for 45 - 48 is 9. So the number of people with 49 correct is \(14 - 9 = 5\)? Wait, no, maybe the intervals are: 45 (2), 46 (4 - 2 = 2), 47 (8 - 4 = 4), 48 (9 - 8 = 1), 49 (14 - 9 = 5), 50 (20 - 14 = 6). Wait, but the question is how many people answered 49 correctly. So the cumulative frequency up to 48 is 9, and up to 49 is 14. So the frequency for 49 is \(14 - 9 = 5\)? Wait, no, maybe I misread. Wait, the x - axis: the first bar is 45 (cumulative 2), then 45 - 46 (cumulative 4), 45 - 47 (8), 45 - 48 (9), 45 - 49 (14), 45 - 50 (20). So the number of people with 49 correct is the cumulative frequency at 45 - 49 minus cumulative frequency at 45 - 48. So \(14 - 9 = 5\)? Wait, no, maybe the intervals are 45, 46, 47, 48, 49, 50. The cumulative frequencies: 45: 2, 46: 4, 47: 8, 48: 9, 49: 14, 50: 20. So the number of people with 49 correct is \(14 - 9 = 5\)? Wait, no, 45 - 49 cumulative is 14, 45 - 48 cumulative is 9. So the frequency for 49 is \(14 - 9 = 5\)? Wait, but let's check again. The problem says "how many people answered 49 questions correctly". So the cumulative frequency up to 48 is 9, and up to 49 is 14. So the number of people with 49 correct is \(14 - 9 = 5\)? Wait, maybe I made a mistake. Wait, the bars: first bar (45) has height 2, second (45 - 46) height 4 - 2 = 2, third (45 - 47) height 8 - 4 = 4, fourth (45 - 48) height 9 - 8 = 1, fifth (45 - 49) height 14 - 9 = 5, sixth (45 - 50) height 20 - 14 = 6. So the number of people with 49 correct is 5? Wait, but let's confirm. The cumulative frequency at 45 - 49 is 14, which means all people with 45 - 49 correct. The cumulative frequency at 45 - 48 is 9, which means all people with 45 - 48 correct. So the difference is the number of people with 49 correct. So \(14 - 9 = 5\).

Step1: Identify cumulative frequency for 48 or less

From the histogram, the cumulative frequency for the interval up to 45 - 48 is 9. This represents the number of people who scored 48 or less (since the cumulative frequency up to 45 - 48 includes all scores from 45 up to 48).

Answer:

5

Part C