1. A bakery has the following probability distribution for the daily demand for its cakes. Using the first column of random numbers in, generate 20 samples from this distribution and construct a histogram of the results. 2. Suppose that we conduct an experiment in which samples of size n are generated from a normal distribution having a known standard deviation s . If we compute the range of each sample, we can estimate the distribution of the statistic R / s . The expected value of this statistic is a factor that statisticians have labeled as d2 . If we know this value and a sample range, then we can estimate s by R / d2 . The values of d2 are shown below for sample sizes from 2 through 5. Develop a sampling experiment on a spreadsheet to estimate these values of d2 by generating 1,000 samples of n random variates from a normal distribution with a mean of 0 and standard deviation of 3 (using the Excel function NORMINV). For each of the 1,000 samples, compute the range, and the value of R / s. Use the average value of R / s to estimate d2 for sample sizes n = 2 through 5. Compare your results to published factors shown above. How well did your experiment perform?
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