Consider Example 18.4-2. In each of the following cases, first write the answer algebraically, and then use excelPoissonQ.xls or TORA to provide numerical answers.

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(a) The probability that the stock is depleted after 3 days.

(b) The average number of dozen roses left at the end of the second day.

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(c) The probability that at least one dozen is purchased by the end of the fourth day, given that the last dozen was bought at the end of the third day.

(d) The probability that the time remaining until the next purchase is at most half a day, given that the last purchase occurred a day earlier.

(e) The probability that no purchases will occur during the first day.

(f) The probability that no order will be placed by the end of the week.