Question

The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 28.7 years, with a standard deviation of 3.7 years. The winner in one recent year was 22 years old Transform the age to a z-score.​

Answer 1

Answer:

$z=-1.81$

Step-by-step explanation:

We have been given that the ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 28.7 years, with a standard deviation of 3.7 years.

To transform the age of a 22 years old winner to a z-score we will use z-score formula.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{ z-score}$,

$x=\text{ Sample score}$,

$\mu=\text{ Mean}$,

$\sigma=\text{ Standard deviation}$.

Upon substituting our given values in z-score formula we will get,

$z=\frac{22-28.7}{3.7}$

$z=\frac{-6.7}{3.7}$

$z=-1.81081=\approx -1.81$

Therefore, the z-score corresponding to the age of a 22 years old winner is -1.81.