The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.2 years, with a standard deviation of 3.5 years. The winner in one recent year was 23 years old.

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

(b) Interpret the results.

(c) Determine whether the age is unusual.

a. z-score = - 1.2

b. The age 23 years old is - 1.2 standard deviations below the mean

c. The age is not unusual

Step-by-step explanation:

a. Transformation to z-score

Mathematically;

z-score = (x - μ) / σ

where σ and μ are the standard deviation and the mean respectively.

From the question, x = 23, μ = 27.2 and σ = 3.5

Let's put these into the equation;

z-score = (23-27.2) / 3.5 = - 1.2

b. Interpretation of result

The interpretation is that 23 years old is - 1.2 standard deviations below the mean

c. Determination

The age is not unusual. This is because any z-value below - 2 or above 2 is considered unusual

-1.2 is above - 2 and thus it is not unusual