A casino operator has invented a new game of "skill" and chance called Grab All You Can. Here's how it works: a contestant reaches his right hand into a jar of dimes and grabs as many as he can in one handful. Then he does the same thing with his left hand in a jar of quarters. Research with many volunteers has determined that the mean number of dimes drawn is 68 with a standard deviation of 9.5, and the mean number of quarters is 42, with a standard deviation of 5.8.
(a) If D=the amount of money, in dollars, that a randomly-selected contestant grabs from the "dime grab," find the mean and standard deviation of D.
(b) If T=the total amount of money, in dollars, that a contestant grabs from both jars, find the mean and standard deviation of T.
(c) The casino operator plans to charge $20 for one round of play (that is, one grab from each jar). If G=how much the contestant gains from one round of play, find the mean and standard deviation of G.
Please show your work.