Final answer:
A graph illustrating a distribution that is skewed to the right will show a descending curve from left to right with a longer tail extending to the higher values. The mode is on the left of the median, and the mean is greater than the median due to the spread of higher values.
Step-by-step explanation:
To select the graph that best illustrates a distribution shape skewed to the right, one should look for certain characteristics. A graph skewed to the right typically has a tail that extends to the right. This means there are a number of higher data values, which causes the mean to be greater than the median, and the mode will be to the left of the median. When you draw a smooth curve through the tops of the bars of a histogram representing such a distribution, the curve will descend from left to right, with most data concentrated on the left side of the graph, and a long tail extending towards the right side.
The correct graph for a right-skewed distribution will show the frequency on the vertical axis, and the horizontal axis will represent the data points or intervals. The bars will start higher on the left and gradually get lower as you move to the right, indicating fewer occurrences of higher values. Additionally, in the context of the chi-square distribution, which is always skewed to the right, we would observe a similar pattern, especially when the degrees of freedom are less than 90.
In summary, to describe the general shape of the curve for data that is skewed to the right, you would note that most of the data points cluster at the lower end of the scale, and as values increase, the frequency of these values decreases, creating a long tail extending to the higher end of the scale.