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\begin{tabular}{l|l|} The distribution is & (Choose one) \\ & \( \begin{array}{l}\text { somewhat negatively skewed } \\ \text { approximately normal } \\ \text { somewhat positively skewed }\end{array} \) \\ \hline\end{tabular}

Ask by Park Carroll. in the United States
Mar 10,2025

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The distribution is approximately normal.

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1. First, we recall that a probability distribution can be classified by its skewness. If most of its values cluster to one side with a tail on the other, it is said to be skewed. - If the tail extends further to the right, the distribution is positively skewed. - If the tail extends further to the left, the distribution is negatively skewed. 2. In contrast, if the data are balanced about a central point with a bell‐shaped curve, then the distribution is approximately normal (symmetric). 3. Without additional specific details (such as a histogram, descriptive statistics, or values like the mean, median, and mode), we typically look at the context or description provided in the problem. In many textbook problems when a distribution is described without noting any obvious asymmetry, it is common to assume that the distribution is approximately normal. 4. Thus, based on the usual interpretation when no additional skew details are given, we choose \[ \text{approximately normal}. \]

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The concept of skewness refers to the asymmetry of a distribution. A somewhat negatively skewed distribution implies that the tail on the left side is longer or fatter than the right side, indicating that most of the data points are clustered on the higher end of the scale, with some lower values pulling the mean to the left. On the other hand, a distribution that is approximately normal follows a bell-shaped curve, meaning it is symmetric around the mean. In this case, the mean, median, and mode are all equal, and the data points are evenly distributed on both sides, making it ideal for many statistical analyses.

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