Question

many students arrived late to carmens orchestra class yesterday. carmens friend ethan, who plays the cello, claimed that violinists were more likely than cellists to arrive late.

carmen surveyed all the violinists and cellists in her orchestra class to find out if ethan was correct.

	on time	late
cellists	3	6

complete the paragraph to explain if the data that carmen collected supports ethans claim.

approximately __ of the violinists arrived late. approximately of the cellists arrived late. so, the data __ ethans claim.

Explanation:

Step1: Calculate total violinists

Total violinists = On time + Late = \( 8 + 13 = 21 \)

Step2: Calculate late percentage for violinists

Percentage of late violinists = \( \frac{13}{21} \approx 0.619 \) or \( 61.9\% \)

Step3: Calculate total cellists

Total cellists = On time + Late = \( 3 + 6 = 9 \)

Step4: Calculate late percentage for cellists

Percentage of late cellists = \( \frac{6}{9} \approx 0.667 \) or \( 66.7\% \)

Step5: Compare percentages

Since \( 61.9\% < 66.7\% \), the percentage of late violinists is less than that of cellists. Wait, no, wait: Wait, \( \frac{13}{21} \approx 0.619 \) (61.9%) and \( \frac{6}{9} \approx 0.667 \) (66.7%)? Wait, no, that can't be. Wait, no, 13/21 is approximately 0.619, 6/9 is approximately 0.667. Wait, but that would mean cellists are more likely? But maybe I miscalculated. Wait, no: Wait, violinists: 8 on time, 13 late. Total violinists: 8 +13=21. So late percentage: 13/21 ≈ 0.619 (61.9%). Cellists: 3 on time, 6 late. Total cellists: 3+6=9. Late percentage: 6/9 ≈ 0.667 (66.7%). Wait, but that would mean cellists are more likely to be late. But that contradicts Ethan's claim. Wait, maybe I made a mistake. Wait, no, let's recalculate. Wait, 13 divided by 21: 13 ÷21 ≈0.619. 6 ÷9=0.666... So 61.9% vs 66.7%. So the percentage of late violinists is less than late cellists? But that would mean Ethan's claim is wrong. But maybe I messed up the total. Wait, no, the table is Violinists: On time 8, Late 13. So total 21. Cellists: On time 3, Late 6. Total 9. So late percentage: violinists 13/21 ≈61.9%, cellists 6/9≈66.7%. So the data does not support Ethan's claim? Wait, but maybe I made a mistake. Wait, no, let's check again. Wait, 13 out of 21 is about 61.9%, 6 out of 9 is about 66.7%. So cellists are more likely to be late. So the data does not support Ethan's claim. But wait, maybe the question is different. Wait, the problem says "violinists were more likely than cellists to arrive late". So we need to check if P(late | violinist) > P(late | cellist). Let's compute P(late | violinist) = 13/(8+13) =13/21≈0.619. P(late | cellist)=6/(3+6)=6/9≈0.667. So 0.619 < 0.667. So the probability of being late is higher for cellists. So the data does not support Ethan's claim. But wait, maybe I miscalculated. Wait, 13 divided by 21: 13 ÷21 ≈0.619, 6 ÷9=0.666... So yes, cellists have a higher late percentage. So the first blank: approximately 62% (or 13/21≈0.619, so 62% or 61.9%), the second blank: approximately 67% (or 66.7%), and the third blank: does not support. Wait, but maybe the problem expects rounding to the nearest whole number or a different approximation. Let's see: 13/21 ≈0.619, which is approximately 62% or 0.62. 6/9=2/3≈0.666..., which is approximately 67% or 0.67. So:

Approximately 62% (or 0.62) of the violinists arrived late. Approximately 67% (or 0.67) of the cellists arrived late. So, the data does not support Ethan's claim.

Wait, but maybe I made a mistake in the total. Wait, violinists: 8 on time, 13 late. So total 21. Cellists: 3 on time, 6 late. Total 9. So late percentage: violinists 13/21 ≈0.619, cellists 6/9≈0.667. So yes, cellists are more likely. So the data does not support Ethan's claim.

Answer:

Approximately \( \boldsymbol{62\%} \) (or \( \boldsymbol{\frac{13}{21} \approx 0.62} \)) of the violinists arrived late. Approximately \( \boldsymbol{67\%} \) (or \( \boldsymbol{\frac{6}{9} \approx 0.67} \)) of the cellists arrived late. So, the data \( \boldsymbol{\text{does not support}} \) Ethan's claim.