Log onto website where you can observe your service bill for the last 12 months (electric bill, cell phone bill, water bill, etc.). If you do NOT feel comfortable sharing this data, you can make up values. 1. In excel, list the values of your bill for the last 12 months on one column.
2. Find the sample mean and sample standard deviation of your data.
3. Pick three bills from the last 12 months and change the values into z-scores. What does the z-score tell you about that particular month?
Analysis
1. Between what two values would be considered a normal bill? Remember, being within 2 Standard Deviations is considered normal.
2. Are any of your bills in the last 12 months unusual? Very unusual?
3. Are there times when you would accept an "unusual" bill? Explain.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.