Skewness measures the asymmetry of a distribution; a perfectly symmetric distribution has skewness 0. Options a. -1 and c. -0.1 imply negative skewness, which is not characteristic of a normal distribution. Hence, the correct answer is d. none of the above, as none of the given values accurately represents the expected skewness in an approximately normal distribution.
In a normal distribution, the mean, median, and mode are all equal and located at the center, resulting in a symmetric bell-shaped curve. Skewness measures the extent and direction of skew (asymmetry) in the distribution. A perfectly symmetric distribution has skewness equal to zero. Negative skewness indicates a longer left tail, while positive skewness indicates a longer right tail. Since the question specifies an approximately normal distribution, we expect skewness to be close to zero. Option b. 0.5 implies positive skewness, which contradicts the characteristics of a normal distribution. Options a. -1 and c. -0.1 indicate negative skewness, which is also inconsistent with the expected symmetry of a normal distribution. Therefore, the correct answer is d. none of the above, as none of the provided values accurately reflects the typical skewness of an approximately normal distribution.