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 3.4 years. the winner in one recent year was 34 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 = 1.56\\)
(type an integer or decimal rounded to two decimal places as needed.)

(b) interpret the results.
an age of 34 is standard deviation(s) below/above 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

$$
LATEXBLOCK0
$$

Interpret the z-score

Using the Z-Score Interpretation knowledge point
An age of 34 is \(1.56\) standard deviations above the mean.

Answer:

An age of 34 is <blank>1.56</blank> standard deviation(s) <blank>above</blank> the mean.