How can I find how many standard deviations away from the mean a value is by using the empirical rule?

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

197 − 46 = 151 197 + 46 = 243

The range of numbers is 151 to 243

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

197 − 2 ⋅ 46 = 105 197 + 2 ⋅ 46 = 289

The range of numbers is 105 to 289

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

197 − 3⋅ 46 = 59 197 + 3 ⋅ 46 = 335

The range of numbers is 59 to 335

Finally, we can use the symmetry of the bell curve to further divide up the percentages.

2.35% of the data values will lie between 59 and 105

13.5% of the data values will lie between 105 and 151

34% of the data values will lie between 151 and 197

34% of the data values will lie between 197 and 243

13.5% of the data values will lie between 243 and 289

2.35% of the data values will lie between 289 and 335

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step-by-step explanation: