In order to understand the prehistory of the Hawaiian island of Lana'i better, anthropologists Maria Sweeney, Melinda Allen, and Boyd Dixon used radiocarbon dating on charcoal found in an ancient dwelling site, the Kaunolu Village National Historic Landmark, the largest archeological complex on the island. In one of their samples, they found that approximately 94% of the original carbon 14 remained.

Using the fact that Carbon 14 decays by 1.202% every 100 years, determine the approximate age of this sample.

In your word document, paste the Excel table you made to come up with your answer.

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.