Final answer:
The appropriate graph for representing the probability of fat calorie consumption being more than 40% is a histogram, which shows frequency distribution and can represent normal distributions. The histogram, combined with its smooth frequency curve, accurately depicts this probability and the correct answer is option C) A, D.
Step-by-step explanation:
To find the probability that the percent of fat calories a person consumes is more than 40%, the correct type of graphical representation would be a histogram. The histogram allows for the visualization of frequency distribution over a continuous interval or certain periods, showing how many data points fall into various ranges. In this case, it can illustrate the frequency of individuals consuming certain percentages of fat calories, from which we can determine the proportion of people above a specific threshold, here being 40%. Each bar in the histogram represents a range of percentage values of fat calories, and the height of each bar indicates how many people fall within that range.
As we know from the given information, the distribution of fat calories is normally distributed, and a histogram is well-suited for representing normal distributions. To determine the probability in question, one would calculate the area under the curve (of the histogram's smooth frequency curve) to the right of the 40% mark. The probability can be visually interpreted by shading the area under the curve that is beyond the 40% line, which is the cut-off point in question. This shaded area represents the proportion of the total number of observations that falls above 40% fat calories consumption.
In conclusion, the correct graph for representing the probability of fat calorie consumption being more than 40% is a histogram. Therefore, the correct option would be C) A, D, indicating that the probability distribution can be represented using both a histogram and its corresponding line graph (smooth curve), but the histogram is essential here.