Solution: Finding z-Scores The distribution of the ages of

Step 1 of 3

(a) The distribution of the ages of the winners of the Tour de France from 1903 to 2012 is approximately bell-shaped.

The mean age is 28.1 years, with a standard deviation of 3.4 years.

We are asked to transform the age to a \(z-\text { score }\)

\(\begin{array}{|l|c|c|} \hline \text { Winner } & \text { Year } & \text { Age } \\ \hline \text { Henri Cornet } & 1904 & 20 \\ \hline \end{array}\)

The standard score, or \(z-\text { score }\), represents the number of standard deviations a value \(x\) lies from the mean \(\mu\). To find the \(z-\text { score }\) for a value, use the formula

\(\begin{array}{l} z=\frac{\text { value }- \text { Mean }}{\text { Standard Deviation }}=\frac{x-\mu}{\sigma} \\ z=\frac{20-28.1}{3.4}=-2.382 \end{array}\)

Hence the \(z-\text { score }\) is -2.382