Write and execute a computer program to derive an approximation of the sampling distribution of the variance. Use a random-number generator that generates standard normal deviates with a mean of zero and a variance of one. Generate 1000 samples of size n and compute the variance of each sample. Develop a histogram using the 1000 values and plot both the histogram and the chi-square distribution for (n – 1) degrees of freedom. Determine the number of sample variances that lie in each tail for probabilities of 0.01, 0.025, 0.05, and 0.10. Execute the program for sample sizes of 5, 10, and 25.