Discussion
Approximate percentage of scores that fall within \(\pm\sigma\) (standard deviation) of the mean in a normal distribution is
Answer: B
About 68 per cent of scores lie within one standard deviation of the mean.
For a normal distribution the empirical rule gives the share of the area within one, two and three standard deviations of the mean as about 68.3%, 95.4% and 99.7%. So the interval \(\mu \pm \sigma\) holds roughly 68% of the scores.
34 is the share on one side only, from the mean to \(\mu + \sigma\). 95 is the share within \(\pm 2\sigma\), and 99 is close to the share within \(\pm 3\sigma\) (or exactly the share within about \(\pm 2.58\sigma\)).
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