Question

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Explanation:

Identify the given parameters

Using the Normal Distribution Properties knowledge point

$$
LATEXBLOCK0
$$

Calculate the Z-score

Using the Z-score Calculation knowledge point

$$ Z = \frac{X - \mu}{\sigma} = \frac{36.8 - 32}{1.5} = \frac{4.8}{1.5} = 3.2 $$

Find the cumulative probability

Using the Standard Normal Table knowledge point

$$ P(X < 36.8) = P(Z < 3.2) = 0.9993129 \approx 99.93\% $$

Answer:

• (A) 99.93% (Correct answer)
• (B) 99.87%