i.) Frepeng cummative profer 8. If the average number af vactation doys for each a a selection of varias dyjs for a selection of vanis countries has a mean of 29.4 days and a stayder? deviation of 8.6 find the 2 Scone for the average numbere of vacation dafs in each of thes. Campries. \( \begin{array}{ll}\text { Candta } 26 \text { days } \\ \text { Italy } & 42 \text { days } \\ \text { united states } & 13 \text { days. }\end{array} \)

To determine how far the average vacation days in Canada, Italy, and the United States fall from the mean in terms of standard deviations, we can calculate the z-scores for each country. The formula for a z-score is: \[ z = \frac{(X - \mu)}{\sigma} \] Here, \( X \) is the value to be standardized (the number of vacation days), \( \mu \) is the mean (29.4 days), and \( \sigma \) is the standard deviation (8.6 days). For Canada (26 days): \[ z = \frac{(26 - 29.4)}{8.6} \approx -0.39 \] For Italy (42 days): \[ z = \frac{(42 - 29.4)}{8.6} \approx 1.47 \] For the United States (13 days): \[ z = \frac{(13 - 29.4)}{8.6} \approx -1.92 \] This tells us that vacation days in Canada and the US are below the average, while Italy's vacation days significantly exceed it! Did you know that vacation days can vary widely around the world? Countries like France and Germany often lead with a generous amount of time off, sometimes exceeding 30 days, while the US typically falls short with only about 10-14 days mandated by law! This variance often reflects cultural attitudes toward work-life balance. If you're ever planning a trip, keep these averages in mind! Knowing that countries like Italy offer more vacation days might inspire you to make the most of your travels there. Just imagine soaking in the Italian sun for 42 days—definitely a perk of being a local!