Question

the ages of the winners of a cycling tournament are approximately bell-shaped. the mean age is 28.9 years, with a standard deviation of 3.4 years. the winner in one recent year was 25 years old.

(a) transform the age to a z-score.
(b) interpret the results.
(c) determine whether the age is unusual.

(a) transform the age to a z-score.
\\(z = \square\\)
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Identify the given parameters

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate the z-score

Using the Z-Score Calculation knowledge point

$$
LATEXBLOCK1
$$

Round to two decimal places

Using the Z-Score Calculation knowledge point

$$ z \approx -1.15 $$

Answer:

(a) Transform the age to a z-score.

\(z =\) <blank>\(-1.15\)</blank>

(Type an integer or decimal rounded to two decimal places as needed.)