Final answer:
A graphic representation of a normal distribution is a bell-shaped curve that is symmetric around the mean, where the total area under the curve equals one. The standard normal distribution has mean zero and standard deviation one, and the area under the curve between any two points represents the probability of values falling within that range.
Step-by-step explanation:
A visual (graphic) representation of a normal distribution is typically shown as a bell-shaped curve. This characteristic graph indicates that data near the mean are more frequent in occurrence than data far from the mean. The graph is symmetric about the mean (μ), which also aligns with the median and mode due to this symmetry. The area under the normal distribution curve represents probability and the total area under the curve is equal to one.
The standard normal distribution is a special case with a mean (μ) of zero and a standard deviation (σ) of one. This distribution is used to determine probabilities and percentiles for datasets that follow a normal distribution. For instance, if you want to find the probability that a value lies between one standard deviation above the mean (x = 1) and two standard deviations above the mean (x = 2), you would look for the area under the curve between these two points.
In applications, the normal distribution is used across various fields, such as psychology, business, economics, and sciences, to model real-world phenomena. Instructors can utilize it to determine grades, and it can represent IQ scores and even real estate prices. However, it's critical to note that while the normal distribution is extremely important, it is not suitable for every data set, especially those that are skewed.