Question

Suppose 95% of the data fall between 12.4 and 46.8. Using the empirical rule, gve an estimate of the standard deviation.
Thanks

Answer 1

The empirical rule says that about:

68% of the data falls between +/- 1 standard deviation;

95% of the data falls between +/- 2 standard deviations;

99.7% of the data falls between +/- 3 standard deviations.

You have the second case. This means that

\[46.8 - 12.4\approx4\sigma\rightarrow\sigma \approx8.6\]