Snapshot 2: an expanded Fermi solution based on 1000 random estimates for

between 40,000 and 80,000

Snapshot 3: an expanded Fermi solution based on 1500 random estimates for

between 30,000,000 and 70,000,000

This Demonstration generates estimates of the number of affected individuals or units within the range

minimum to

maximum set by the user with sliders and a popup menu. The ranges of the

probability factors (

from 1 to 6) are specified by

minimum and

maximum and are set by sliders. The number of repeated trials is entered using the top-most slider. The program generates a new dataset when the value of any control other than the clear button is altered. For a new random dataset at the current control settings click "clear" followed by "generate". For scenarios involving fewer than all six

factors, set the unused factor's minimum and maximum values to 1. The panel shows the program controls at their current settings, a histogram of the estimates computed in the repeated trials, and the lognormal distribution having the same logarithmic mean and standard deviation as the generated estimates depicted as a solid red curve. The plot title text includes the analytic solution "best estimate" and the one derived from the lognormal distribution's mode. Estimates for

and

outside their sliders' allowed range of 1 to 1000 can be obtained by setting the "

multiplier" popup menu to the appropriate factor. Notice that if all seven factors' (i.e.,

and the six

's) minimum and maximum values are the same, the program will render the conventional Fermi solution plotted as a spike. Also, if all but one of the seven factors' minimum and maximum values are the same, then the program will generate random estimates with a uniform distribution. In that case, although the program will still generate a corresponding lognormal distribution curve, it may no longer be representative.

M. Peleg, M. D. Normand, J. Horowitz, and M. G. Corradini, "An Expanded Fermi Solution for Microbial Risk Assessment,"

*International Journal of Food Microbiology*,

**113**(1), 2007 pp. 92–101.