A cumulative probability curve is a visual representation of a cumulative distributive function, which is the probability that a variable will be less than or equal to a specified value. Since it is a cumulative function, the cumulative distributive function is actually the sum of the probabilities that the variable will have any of the values less than the stated value. For a function with a normal distribution, the cumulative probability curve will begin at 0 and rise to 1, with the steepest part of the curve in the center, representing the point with the highest probability for the function.

List all of the values for “x.” If “x” is a continuous function, select intervals for “x” and list them instead. The intervals should be evenly spaced, ranging from the least “x” to the highest. Smaller intervals will lead to a smoother and more accurate cumulative probability curve. For example, let the values of “x” equal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Compute the probabilities for each value or interval of “x.” All of the probabilities should be between 0 and 1. If “x” has a normal distribution, the highest probabilities will be at the center of the range and the probabilities at either extreme will be near 0. For the example beginning in Step 1, the respective probabilities for “x” might be 0, 0, 0, .05, .25, .4, .25, .05, 0, 0 and 0.

Compute the cumulative sums for each probability of “x.” The cumulative probability for each value of “x” will be the probability of that “x” plus the probabilities of each preceding “x.” In this example, the respective cumulative probabilities for “x” would be 0, 0, 0, .05, .30, .70, .95, 1.0, 1.0, 1.0 and 1.0. If “x” has a normal distribution, the first values will always be 0. Regardless of the type of distribution, the last value of the cumulative probability function will be 1.

Graph the points for the cumulative distribution function. The horizontal axis should include all values or intervals of “x.” The vertical axis should range from 0 to 1. Connect the points as smoothly as possible. If “x” has a normal distribution, the curve will resemble a stretched “s” shape.

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