Question

1. vacation days if the average number of vacation days for a selection of various countries has a mean of 29.4 days and a standard deviation of 8.6 days, find the z - scores for the average number of vacation days in each of these countries. canada 26 days italy 42 days united states 13 days source: www.infoplease.com

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 29.4$ and $\sigma=8.6$.

Step2: Calculate z - score for Canada

For Canada, $x = 26$. Substitute into the formula: $z_{Canada}=\frac{26 - 29.4}{8.6}=\frac{- 3.4}{8.6}\approx - 0.395$.

Step3: Calculate z - score for Italy

For Italy, $x = 42$. Substitute into the formula: $z_{Italy}=\frac{42-29.4}{8.6}=\frac{12.6}{8.6}\approx1.465$.

Step4: Calculate z - score for United States

For the United States, $x = 13$. Substitute into the formula: $z_{US}=\frac{13 - 29.4}{8.6}=\frac{-16.4}{8.6}\approx - 1.907$.

Answer:

Canada: $z\approx - 0.395$
Italy: $z\approx1.465$
United States: $z\approx - 1.907$