As per empirical rule area under the curve for z value varying from -3 to +3 is________Group of answer choices100%99.7%95%68%

Break Down the Problem

1. Identify the Empirical Rule: The empirical rule states how data is distributed in a normal distribution.
2. Determine the Z-value range: We need to find the area under the curve for Z values from -3 to +3.

Relevant Concepts

3. Understand the Empirical Rule: For a normal distribution:
   • Approximately 68% of the data falls within 1 standard deviation (Z = -1 to +1).
   • Approximately 95% falls within 2 standard deviations (Z = -2 to +2).
   • Approximately 99.7% falls within 3 standard deviations (Z = -3 to +3).

Analysis and Detail

4. Applying the Empirical Rule: For Z values from -3 to +3, according to the empirical rule, we can conclude that about 99.7% of the data falls within this range.

Verify and Summarize

5. Verification through Normal Distribution Tables: Normal distribution tables confirm that the area under the curve for Z values from -3 to +3 corresponds to 99.7%.

Final Answer

The area under the curve for Z values varying from -3 to +3 is 99.7%.