As discussed in the text, it often is possible to use a theoretical distribution as an approx imation 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 halfway-house data again. We calculated the sample mean x- = 380.4 and the sample standard deviation s = 217.6. Taking these as approximately equal to μ and σ, use the Z table in Appendix E to find normal cumulative probabilities for dollar costs of 200, 300, 400, 500, 600, and 700. How do these theoretical normal probabilities compare with the data-based probabilities from the CDF in Figure 10.4? Do you think that the normal distribution is an appropriate distribution to use in this case? You might sketch the normal distribution CDF and superimpose it on Figure 10.4 to obtain a visual feel for how the normal distribution fits the data.