Question

the times of all 15 year olds who run a certain race are approximately normally distributed with a given mean \\(\mu = 18\\) sec and standard deviation \\(\sigma = 1.2\\) sec. what percentage of the runners have times less than 14.4 sec?

\\(\bigcirc\\) 0.15%
\\(\bigcirc\\) 0.30%
\\(\bigcirc\\) 0.60%
\\(\bigcirc\\) 2.50%

Explanation:

Identify given parameters

Using the Normal Distribution knowledge point

$$
LATEXBLOCK0
$$

Calculate the z-score

Using the Z-Score Formula knowledge point

$$ z = \frac{X - \mu}{\sigma} = \frac{14.4 - 18}{1.2} = \frac{-3.6}{1.2} = -3 $$

Apply the Empirical Rule

Using the Empirical Rule knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) 0.15% (Correct answer)
• (B) 0.30%
• (C) 0.60%
• (D) 2.50%