A casino cheat is caught trying to use a pair of loaded dice. At his court trial, physical evidence reveals that some of the black dots were drilled, filled with lead, then repainted to appear normal. In addition to the physical evidence, the dice are rolled in court with these results:

A probability expert testifies that when fair dice are rolled, the mean should be 7.0 and the standard deviation should be 2.4.
a. Find the mean and standard deviation of the sample values obtained in court.
b. Based on the outcomes obtained in court, what is the probability of rolling a 12? How does this result compare to the probability of 1/36 (or 0.0278) for fair dice?
c. If the probability of rolling a 12 with fair dice is 1/36, find the probability of getting at least one 12 when fair dice are rolled 20 times.
d. If you are the defence attorney, how would you refute the results obtained in court?

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