As per empirical rule area under the curve for z value varying from -2 to +2 is________Group of answer choices68%100%95%99.7%

Break Down the Problem

1. Identify the significance of the empirical rule in statistics, specifically regarding a normal distribution.
2. Determine the area under the curve for the specified z-values of -2 and +2.

Relevant Concepts

3. The empirical rule states that:
   • Approximately 68% of data falls within 1 standard deviation (z-values of -1 to +1).
   • Approximately 95% falls within 2 standard deviations (z-values of -2 to +2).
   • Approximately 99.7% falls within 3 standard deviations (z-values of -3 to +3).

Analysis and Detail

4. For z-values from -2 to +2, we specifically refer to the segment of the empirical rule that encompasses the area around the mean. Since -2 and +2 cover a broader range than -1 and +1, we can conclude that the area is larger than 68% but less than 100%.

Verify and Summarize

5. As established from the empirical rule, the area under the curve for z-values ranging from -2 to +2 represents approximately 95% of the total area under the normal distribution curve.

Final Answer

The area under the curve for z values varying from -2 to +2 is 95%.