Question: As discussed in the text, it often is possible to use a theoretical distribution as an approximation of the distribution of some sample data. It is always important, however, to check to make sure that your data really do fit the distribution you propose to use. Consider the solar trash compactor data again. We calculated the sample mean = $1,005 and the sample standard deviation s ¼ $204. Taking these as approximately equal to μ and σ, find the normal cumulative probabilities for operating costs of $700, $800, $900, $1,000, $1,200, and $1,400. How do these theoretical normal probabilities compare with the data-based probabilities from the CDF in Figure 10.7? Do you think that the normal distribution is an appropriate distribution to use in this case? Compare the fit of the normal distribution CDF to the empirical CDF by superimposing them onto one graph.