Question

The left-hand "tail" of the standard normal curve can be defined as the part of it that lies at least two standard deviations to the left of the mean.

According to the Empirical Rule, approximately what percentage of the area under the whole curve is in the left-hand tail? Round your answer to the nearest tenth.

Answer 1

2.5%

Explanation:

The Empirical Rule states that 95% of the values lies between two standard deviations to the left of the mean and two standard deviations to the right of the mean. 50% of the values lies on the left side respect to the mean; so, 95%/2 = 47.5% of the values lies in the region formed two standard deviations to the left of the mean. In consequence, 50% - 47.5% = 2.5% of the values lies on the left-hand "tail" of the standard normal curve.

Answer 2

Roughly 95% of the data lies within 2 standard deviations of the mean.

So (100% - 95%)/2 = 2.5% of the data lies within each tail.

This means roughly 2.5% of the data is in the left hand tail.