Question

the mean and standard deviation of the daily high temperature in three cities for the month of september 2018. the z - score for the high temperature on september 19 in each city, relative to that city’s mean, is given: tokyo: 2.24, sydney: - 0.85, london: - 1.98. which statements correctly compare the z - scores? choose the correct answers. the high temperature on september 19 in tokyo was the most abnormal. the high temperature in tokyo on september 19 was the coldest of the cities. the high temperature in london on september 19 was the warmest of the cities. only tokyo’s high temperature was warmer than its mean. the high temperatures in tokyo and london were colder than the mean, while sydney was warmer. the high temperature on september 19 in sydney was the closest to the mean.

Explanation:

1. Z-scores measure how many standard deviations a value is from the mean. A more extreme (farther from 0) z-score is more abnormal. -2.94 is the most extreme z-score here, so Tempe's temperature is the most abnormal.
2. Negative z-scores mean the value is below the mean (colder than average), positive z-scores mean the value is above the mean (warmer than average). Tempe's z-score (-2.94) is the lowest, so its temperature is the coldest of the three cities.
3. The z-score closest to 0 is the closest to the mean. Ankeny's z-score (0.45) is closer to 0 than -0.98 and -2.94, so its temperature is closest to its city's mean.
4. Lubec has a negative z-score (-0.98), so its temperature was colder than its mean, not warmer.
5. Ankeny has a positive z-score, so its temperature was warmer than its mean, while Tempe and Lubec have negative z-scores, so theirs were colder than their means.

Answer:

• The high temperature on September 19 in Tempe was the most abnormal.
• The high temperature in Tempe on September 19 was the coldest of the cities.
• The high temperature on September 19 in Ankeny was the closest to the mean.