Question

Write a function that computes the limits (symmetrical about the mean) corresponding to a specified normal distribution probability. The arguments to the function are µ, σ and the area, a ∈ [0, 1], between the two limits. The output of the function is a normal probability plot indicating the limits associated with the specified area. Edit the x-axis of the plot to only include labels for xL, µ and xU . Include a text output on the graph indicating the area between the two limits.

Answer 1

The student's assignment involves writing a function to find and plot symmetrical limits around the mean for a given area under a normal distribution, using the mean, standard deviation, and area as inputs to the function.

Step-by-step explanation:

The student's question relates to constructing a function to calculate the symmetrical limits about the mean for a specified area under a normal distribution. Given the distribution's mean (μ), standard deviation (σ), and the desired area (a), the function should output a normal probability plot indicating the two limits xL and xU that encapsulate the specified area. While creating the plot, the X-axis will feature labels only for xL, μ, and xU, and display the given area a textually on the graph.

To achieve this, you would typically use statistical software or a programming language like Python with libraries such as SciPy for calculating the z-scores corresponding to the cumulative area, and libraries like matplotlib for plotting. The steps would involve calculating the z-scores that correspond to the cumulative left tail area of (1-a)/2 and the right tail area of (1+a)/2. Then, these z-scores are converted back to the original scale using the mean and standard deviation. The plot would visually represent the distribution curve, the area of interest, and the relevant labels.