Final answer:
The skewness of a normally distributed set of data is zero, indicating a symmetric distribution with equal tails. Graphing the data or calculating the skewness coefficient can confirm this, and normality is assumed for methods like the Student's t-distribution.
Step-by-step explanation:
To estimate the skewness of a given set of data that is normally distributed, it's important to understand several key concepts. Skewness is a measure of the symmetry, or lack thereof, in a distribution. In a perfectly normal distribution, the mean, median, and mode all coincide at the same point, and the distribution is symmetrical. Therefore, the skewness for a normal distribution is zero, indicating no skew. When data is perfectly normal, visual aids such as histograms or box plots will show a bell-shaped curve, symmetrical around the mean.
However, real-world data might have slight deviations from normality. To check for skewness, we would typically calculate the skewness coefficient using statistical formulas or software. Nonetheless, if we are given that the population is normally distributed or the sample size is large enough to assume normality as per the central limit theorem, the skewness should be very close to zero. If a distribution is skewed to the right, it has a long tail in the positive direction, and the skewness value will be positive. Conversely, if a distribution is skewed to the left, it has a long tail in the negative direction, and the skewness value will be negative. In the case of a normal distribution, you would not need to focus on quartiles or extremes since skewness is absent.
In summary, the skewness for a normal distribution is expected to be zero, indicating a symmetrical distribution with equal tails on both sides. When analyzing data that is assumed to be normal, always graph the data to visually confirm this property. If the analysis involves a Student's t-distribution, as might be the case with smaller sample sizes without a known population standard deviation, normality is assumed. This reinforces that the expectation of skewness being zero holds unless empirical evidence suggests otherwise.