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24 Sep 2025, 09:25
Kudos
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The median stamina score is greater than the median reach.: Yes
Stamina score is directly proportional to reach.: No
If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15.: Yes
The table shows the performance of 15 professional swimmers who entered a county championship. Lap time is the average number of seconds per lap, stamina score is a coach-assigned rating out of 100, and reach is the arm span of a swimmer, measured from the tip of one middle finger to the tip of the other with both arms fully extended.
For each statement, select Yes if it is true based on the table. Otherwise, select No.
| Swimmer | Lap time (sec) | Stamina score | Reach (inches) |
|---|---|---|---|
| Allen | 34.1 | 82 | 74 |
| Barton | 32.8 | 78 | 79 |
| Chen | 31.0 | 69 | 72 |
| Diaz | 36.4 | 92 | 81 |
| Evans | 33.5 | 88 | 70 |
| Foster | 37.2 | 74 | 82 |
| Grant | 35.6 | 71 | 77 |
| Hughes | 30.9 | 85 | 73 |
| Ibrahim | 33.8 | 80 | 78 |
| Jensen | 32.1 | 95 | 76 |
| Kim | 34.9 | 67 | 83 |
| Lopez | 31.3 | 90 | 71 |
| Mason | 36.7 | 79 | 80 |
| Nash | 35.2 | 72 | 75 |
| Olsen | 30.5 | 98 | 84 |
For each statement, select Yes if it is true based on the table. Otherwise, select No.
| Yes | No | |
| The median stamina score is greater than the median reach. | ||
| Stamina score is directly proportional to reach. | ||
| If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15. |
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Official Answer
The median stamina score is greater than the median reach.: Yes
Stamina score is directly proportional to reach.: No
If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15.: Yes
24 Sep 2025, 09:25
Kudos
Bookmarks
Official Solution:
• The median stamina score is greater than the median reach.
With 15 swimmers, the median is the 8th largest value. The stamina scores in order give a median of 80 (8th value). The reaches in order give a median of 77 (8th value). Since 80 > 77, the statement is true.
Answer: Yes
• Stamina score is directly proportional to reach.
If two values are directly proportional, each stamina score divided by reach would give the same ratio. This is not the case here. For example, Diaz has 92/81 ≈ 1.14, while Kim has 67/83 ≈ 0.81. Because the ratios differ, stamina score is not directly proportional to reach.
Answer: No
• If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32.3 seconds or the reach is above 75 inches is 12/15.
Lap time below 32.3: 4 swimmers (Olsen, Hughes, Chen, Lopez).
Reach above 75: 9 swimmers (Jensen, Grant, Ibrahim, Barton, Mason, Diaz, Foster, Kim, Olsen).
However, one swimmer, Olsen, belongs to both lists. So the total count is 4 + 9 − 1 = 12. Probability = 12/15. The statement is true.
Answer: Yes
Correct answer:
The median stamina score is greater than the median reach. "Yes"
Stamina score is directly proportional to reach. "No"
If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15. "Yes"
Bunuel
• The median stamina score is greater than the median reach.
With 15 swimmers, the median is the 8th largest value. The stamina scores in order give a median of 80 (8th value). The reaches in order give a median of 77 (8th value). Since 80 > 77, the statement is true.
Answer: Yes
• Stamina score is directly proportional to reach.
If two values are directly proportional, each stamina score divided by reach would give the same ratio. This is not the case here. For example, Diaz has 92/81 ≈ 1.14, while Kim has 67/83 ≈ 0.81. Because the ratios differ, stamina score is not directly proportional to reach.
Answer: No
• If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32.3 seconds or the reach is above 75 inches is 12/15.
Lap time below 32.3: 4 swimmers (Olsen, Hughes, Chen, Lopez).
Reach above 75: 9 swimmers (Jensen, Grant, Ibrahim, Barton, Mason, Diaz, Foster, Kim, Olsen).
However, one swimmer, Olsen, belongs to both lists. So the total count is 4 + 9 − 1 = 12. Probability = 12/15. The statement is true.
Answer: Yes
Correct answer:
The median stamina score is greater than the median reach. "Yes"
Stamina score is directly proportional to reach. "No"
If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15. "Yes"
