Bunuel
A consumer electronics company asked 200 participants who had tested a new smartphone to evaluate five of its features. For each feature, a participant could give one of four ratings: Excellent, Good, Fair, or Poor. No other rating options were available, and no participant could give more than one rating to the same feature. Some participants did not rate every feature. The table shows the percentage of all 200 participants who gave each rating.
| Feature | Excellent | Good | Fair | Poor |
|---|
| Battery life | 31% | 39% | 16% | 8% |
| Camera quality | 28% | 34% | 18% | 12% |
| Display brightness | 22% | 41% | 20% | 11% |
| Speaker quality | 16% | 29% | 31% | 17% |
| Device weight | 37% | 33% | 12% | 10% |
For each of the following questions, select
Can be determined if the answer can be determined from the information provided. Otherwise, select
Cannot be determined.
Official Solution:
• What percentage of participants who gave a rating for battery life rated it either Excellent or Good?For battery life, the percentage of all participants who gave a rating was:
31% + 39% + 16% + 8% = 94%
Since there were 200 participants:
200 * 94% = 188 participants gave a rating for battery life.
The number who rated battery life either Excellent or Good was:
200 * (31% + 39%) = 140
Therefore, among those who gave a rating, the required percentage is:
140/188 ≈ 74.5%
So the answer can be determined.
Answer:
Can be determined.
• Did more than 30 participants rate both camera quality and device weight Excellent?56 participants rated camera quality Excellent:
200 * 28% = 56
and 74 participants rated device weight Excellent:
200 * 37% = 74
However, the table does not indicate how many participants belong to both groups. The overlap could be as small as 0 and as large as 56, if all 56 participants who rated camera quality Excellent also rated device weight Excellent.
Since the overlap could be either less than or greater than 30, the answer cannot be determined.
Answer:
Cannot be determined.
• Which had the greater percentage of participants who gave no rating: display brightness or speaker quality?For display brightness, the percentages shown total:
22% + 41% + 20% + 11% = 94%
So 6% gave no rating.
For speaker quality:
16% + 29% + 31% + 17% = 93%
So 7% gave no rating.
Therefore, speaker quality had the greater percentage of participants who gave no rating.
Answer:
Can be determined.