Provide an appropriate response. If nothing is known about the shape of a distribution, what percentage of the observations fall within 2 standard deviations of the mean? A) at least \( 75 \% \) B) at most \( 25 \% \) C) approximately \( 5 \% \) D) approximately \( 95 \% \)

When nothing is known about the shape of a distribution, we can refer to the empirical rule (also known as the 68-95-99.7 rule) which applies to normal distributions. According to this rule: - Approximately \( 68\% \) of the observations fall within 1 standard deviation of the mean. - Approximately \( 95\% \) of the observations fall within 2 standard deviations of the mean. - Approximately \( 99.7\% \) of the observations fall within 3 standard deviations of the mean. Since the question specifies that nothing is known about the shape of the distribution, we can still use the empirical rule as a guideline for a normal distribution. Thus, the correct answer is: **D) approximately \( 95 \% \)**.