Question

use the empirical rule to find a reasonable estimate for p(z ≤ 0.82). 10% 30% 50% 80% done standard normal distribution z = 0.82

Explanation:

Step1: Recall Empirical Rule

The empirical rule (68 - 95 - 99.7 rule) for normal distribution: ~68% data within \( z=\pm1 \), ~95% within \( z=\pm2 \), ~99.7% within \( z=\pm3 \). For \( z = 0.82 \) (close to \( z = 1 \)), the area to the left of \( z = 0.82 \) should be more than 50% (since mean \( \mu = 0 \) in standard normal, left of 0 is 50%) and less than the area left of \( z = 1 \) (which is \( 50\%+\frac{68\%}{2}=84\% \) approximately).

Step2: Evaluate Options

• 10%: Too low (left of 0 is 50%).
• 30%: Too low.
• 50%: Left of 0 is 50%, but \( z = 0.82>0 \), so area should be more than 50%.
• 80%: Close to 84% (area left of \( z = 1 \)), so 80% is reasonable.

Answer:

80%