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 x = $1,005 and the sample standard deviation s = $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 CDFin Figure 10.7? Do you think that the normal distribution is an
Figure 10.7

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P Yearly Profit -$25,000) 0.00 P Yearly Profit -$10,000) 0.10 P Yearly Profit SO) 0.30 P(Yearly Profit $15.000) 0.75 P Yearly Profit $24.000) 1.00