Answer :
In a normal distribution, certain percentages of data fall within specific ranges, measured in terms of the standard deviation (σ) from the mean (μ). The distribution follows a predictable pattern:
1. 68% of the data falls within 1 standard deviation from the mean ([tex]\(\mu \pm \sigma\)[/tex]).
2. 95% of the data falls within 2 standard deviations from the mean ([tex]\(\mu \pm 2\sigma\)[/tex]).
3. 99.7% of the data falls within 3 standard deviations from the mean ([tex]\(\mu \pm 3\sigma\)[/tex]).
Given that we are interested in the range within which 95% of the data falls, we use the empirical rule (also known as the 68-95-99.7 rule) to determine that:
95% of the data in a normal distribution falls within 2 standard deviations from the mean.
Thus, the correct range is:
[tex]\[ \mu \pm 2\sigma \][/tex]
Therefore, the correct answer is:
[tex]\[ \mu \pm 2\sigma \][/tex]
1. 68% of the data falls within 1 standard deviation from the mean ([tex]\(\mu \pm \sigma\)[/tex]).
2. 95% of the data falls within 2 standard deviations from the mean ([tex]\(\mu \pm 2\sigma\)[/tex]).
3. 99.7% of the data falls within 3 standard deviations from the mean ([tex]\(\mu \pm 3\sigma\)[/tex]).
Given that we are interested in the range within which 95% of the data falls, we use the empirical rule (also known as the 68-95-99.7 rule) to determine that:
95% of the data in a normal distribution falls within 2 standard deviations from the mean.
Thus, the correct range is:
[tex]\[ \mu \pm 2\sigma \][/tex]
Therefore, the correct answer is:
[tex]\[ \mu \pm 2\sigma \][/tex]
