The weights (to the nearest pound) of some boxes to be shipped are found to be: Weight 65 68 69 70 71 72 90 95 frequency 1 2 5 8 7 3 2 2 Explain why or why not this could be represented by a bell curve (a normal distribution).

The given weights do not exhibit the characteristics of a bell curve or a normal distribution. The data is skewed, lacks a clear central tendency, and contains outliers. Therefore, it cannot be accurately represented by a normal distribution.

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To determine whether the given weights can be represented by a bell curve (normal distribution), we need to assess if the data exhibits the characteristics of a normal distribution.

Here are a few considerations:

Symmetry: A normal distribution is symmetric, meaning the data is equally distributed around the mean. In the given data, there are more observations on one side of the distribution (higher weights) than the other. This indicates a lack of symmetry, which is not characteristic of a bell curve.

Central tendency: A normal distribution typically has a single peak or mode at the center. In this case, there isn't a clear central tendency as the weights seem to be spread across different ranges without a dominant peak.

Outliers: Normal distributions tend to have minimal outliers or extreme values. The presence of weights like 90 and 95, which are noticeably higher than the other values, suggests the presence of outliers. This goes against the assumption of a bell curve.

Based on these considerations, it appears that the given weights do not exhibit the characteristics of a bell curve or a normal distribution. The data is skewed, lacks a clear central tendency, and contains outliers. Therefore, it cannot be accurately represented by a normal distribution.

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