Question

question 31 points 3

a set of final examination grades in a statistics course was found to be normally distributed with a mean of 73 and a standard deviation of 8. what percentage of students scored between 65 and 89?

81.95%
84.13%

Explanation:

Identify the given parameters

Using the Normal Distribution Properties knowledge point

$$
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$$

Calculate the Z-scores for the boundaries

Using the Z-score Calculation knowledge point

$$
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$$

Determine the interval probability

Using the Empirical Rule and Interval Probability knowledge points

$$
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$$

Using standard normal table values:

$$
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$$

Comparing with the closest option:

$$ 81.95\% \approx 81.86\% \text{ (using standard approximations)} $$

Answer:

• (A) 81.95% (Correct answer)
• (B) 84.13%