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 = -1.15\\)
(type an integer or decimal rounded to two decimal places as needed.)

(b) interpret the results.
an age of 25 is standard deviation(s) below the mean.
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Calculate the z-score

Using the Z-Score Calculation knowledge point

$$ z = \frac{x - \mu}{\sigma} = \frac{25 - 28.9}{3.4} = \frac{-3.9}{3.4} \approx -1.15 $$

Interpret the z-score

Using the Z-Score Interpretation knowledge point
An age of 25 has a z-score of \(-1.15\). This means the value lies \(1.15\) standard deviations below the mean.

Answer:

Question 1

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

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

Question 2

(b) Interpret the results.

An age of 25 is <blank>1.15</blank> standard deviation(s) <blank>below</blank> the mean.