Question

In a standard normal distribution 95% of the data is within +/- _____ standard deviations of the mean.

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Answer 1

95% fall between -2 and 2 (within 2 standard deviations of the mean) .

Answer 2

In a standard normal distribution 95% of the data is within +/- 2 standard deviations of the mean.

Solution-

The Empirical Rule (68-95-99.7%)-

This rule tells us that

1. around 68% of the data will fall within one standard deviation of the mean
2. around 95% of the data will fall within two standard deviations of the mean
3. around 99.7% of the data will fall within three standard deviations of the mean.

Therefore, in a standard normal distribution 95% of the data is within +/- 2 standard deviations of the mean.