1. Problem: Compare performances using z-scores. 1.a) Ping's z-score = 1.60, Pong's z-score = 1.75. Since a higher z-score means better performance relative to the mean, Pong performed better. 1.b) Sol's z-score = -1.5, Buddy's z-score = -2.0. Since a higher z-score is better, Sol performed better than Buddy. 2. Problem: Find z-scores given student grades, mean = 81, SD = 5. Formula: $$z=\frac{X-\mu}{\sigma}$$ where $X$ = grade. 2.a) Leand: $$z=\frac{70-81}{5} = \frac{-11}{5} = -2.2$$ 2.b) Louis: $$z=\frac{91-81}{5} = \frac{10}{5} = 2.0$$ 2.c) Chris: $$z=\frac{60-81}{5} = \frac{-21}{5} = -4.2$$ 2.d) Leo: $$z=\frac{85-81}{5} = \frac{4}{5} = 0.8$$ 2.e) Evelyn: $$z=\frac{96-81}{5} = \frac{15}{5} = 3.0$$ 3. Problem: Find grades given z-scores, mean = 81, SD = 5. Formula: $$X=\mu + z\times \sigma$$ 3.a) Pepe, $z=1$: $$X = 81 + 1 \times 5 = 86$$ 3.b) Ding, $z=-2$: $$X = 81 + (-2) \times 5 = 81 - 10 = 71$$ 3.c) Lorna, $z=-2.5$: $$X = 81 + (-2.5) \times 5 = 81 - 12.5 = 68.5$$ 3.d) Sam, $z=1.25$: $$X = 81 + 1.25 \times 5 = 81 + 6.25 = 87.25$$ 3.e) Lito, $z=2.35$: $$X = 81 + 2.35 \times 5 = 81 + 11.75 = 92.75$$ 4. Problem: Compare Michael's performances in 30th and 31st NBA seasons for scoring 26 points. Calculate z-scores: Season 30: Mean = 24, SD = 6 $$z = \frac{26 - 24}{6} = \frac{2}{6} = 0.33$$ Season 31: Mean = 19, SD = 5 $$z = \frac{26 - 19}{5} = \frac{7}{5} = 1.4$$ Higher z-score means better performance relative to the season's average, so Michael performed better in the 31st season. 5. Problem: Find Robin's earnings given z = -0.91, mean = 540, SD = 11. Formula: $$X = \mu + z \times \sigma = 540 + (-0.91) \times 11 = 540 - 10.01 = 529.99$$ Final answer: Robin earned approximately 530 on that day.