Question

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.

Answer 1

Part(a): The value of the Z-score is -1.2

Part(b): The age of the winner is -1.2 standard deviation from the mean.

Part(c): Yes, the age is unusual.

Given,

$\mu =27.2\\\sigma = 3.5$

Winner age, X = 23

Part(a):

The formula for the Z-score is,

$Z=\frac{x-\mu }{\sigma } \\=\frac{23-27.2}{3.5}\\=-1.2$

Part(b): The age of the winner is -1.2 standard deviation from the mean which is equal to its Z-score value.

Part(c): Yes, the age is unusual.

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