64. Which distribution would have a mean and median that are approximately equal after an analysis of each employee’s number of customer service calls over the last month?
Answer: D
The distribution that would have a mean and median that are approximately equal is the Normal distribution.
In a Normal distribution, the data is symmetrically distributed around the mean, which means that the mean and median will be approximately equal. This characteristic is a defining property of Normal distributions.
A) Pareto distribution
The Pareto distribution is generally skewed to the right, which means that its tail extends toward higher values. This results in a significant difference between the mean and median, making this option incorrect.
B) Multimodal distribution
A multimodal distribution can have multiple peaks and may not exhibit symmetry. Depending on the distribution's shape, the mean and median can vary significantly, thus this option does not guarantee that the mean and median would be approximately equal.
C) Bimodal distribution
Similar to the multimodal distribution, a bimodal distribution has two peaks and can also be asymmetrical. The presence of two modes can lead to discrepancies between the mean and median, making this option unsuitable as well.
D) Normal distribution
The Normal distribution is characterized by its symmetry around the mean. In this type of distribution, the mean and median are equal, making it the correct choice for the question.
Conclusion
The Normal distribution is the only option among the choices that ensures the mean and median remain approximately equal due to its symmetrical nature. All other distributions listed either exhibit skewness or multiple modes, which disrupt the balance necessary for equality between the mean and median.