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) the mean.
(type an integer or decimal rounded to two decimal places as needed.)
above
below

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 25 is \(1.15\) standard deviations below the mean, because the z-score is \(-1.15\).

Determine if the age is unusual

Using the Normal Distribution Outliers knowledge point
An observation is typically considered unusual if its z-score is less than \(-2\) or greater than \(2\). Since \(-1.15\) is between \(-2\) and \(2\), the age of 25 is not unusual.

Answer:

Question 1

\(z = -1.15\)

Question 2

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

Question 3

The age is <blank>not unusual</blank> because its z-score is between \(-2\) and \(2\).