By the empirical rule, how many students in a class of $200$ would score within the range $\mu \pm 2\sigma$?

• A. $190$
• B. $136$
• C. $150$
• D. $68$

Answer: (A)

Verified step by step guidance

1. Recall the empirical rule (68-95-99.7 rule), which states that for a normal distribution: approximately 68% of data falls within 1 standard deviation (\(\mu \pm \sigma\)), approximately 95% falls within 2 standard deviations (\(\mu \pm 2\sigma\)), and approximately 99.7% falls within 3 standard deviations (\(\mu \pm 3\sigma\)).
2. Identify that the problem asks for the number of students scoring within \(\mu \pm 2\sigma\), which corresponds to about 95% of the data according to the empirical rule.
3. Calculate 95% of the total number of students in the class. Since there are 200 students, multiply 200 by 0.95: \$200 \times 0.95$.
4. Interpret the result as the approximate number of students scoring within the range \(\mu \pm 2\sigma\).
5. Compare your calculated number to the given answer choices to select the closest value.