Final answer:
The scores described would produce a positively skewed distribution, due to the presence of an outlier pulling the mean upwards. This distribution differs from a normal bell curve distribution, which is symmetrical and has the mean, median, and mode all at the same point.
Step-by-step explanation:
If a data set includes outliers, it can significantly influence the distribution shape. With the data provided indicating a mean that is positively pulled by an extreme outlier (for example, 90), we would observe a positively skewed distribution. This right-skewness is characterized by more low scores than high scores, with a tail that stretches towards the higher values.
The properties of a normal distribution are distinct, and a bell curve is said to be symmetrical, with the mean, median, and mode all coinciding at the same point. However, in this case, the presence of outliers and a skewed distribution suggests that we are not dealing with a normal distribution. This can be contrasted with a normal bell curve distribution, where the data would be symmetrically distributed about the mean.
According to Chebyshev's Rule, a certain proportion of data falls within a certain number of standard deviations from the mean, regardless of distribution shape. This still holds true for skewed distributions. In the context of positively skewed data, one might observe a clustering of data within the lower range and an elongated tail towards higher values, which is evident from the data set provided.
When constructing a stem plot for the range zero-100, one should list the tens digits as the stem and the units digits as the leaves. This visual representation will help to further highlight the skewness of the data. If the data is skewed positively, the leaves will display a longer stretch to the right with potentially fewer leaves on the higher stems (indicating an outlier).