Probability problems for binomial and normal variable

1.) Listed below is the percent increase in sales for the MG Corporation over the last 5 years. Determine the geometric mean percent increase in sales over the period. (See attached)

2.) In 1996 a total of 14,968,000 taxpayers in the United States filed their individual tax returns electronically. By the year 2002 the number increased to 46,282,200. What is the geometric mean annual increase for the period?

3.) The events X and Y are mutually exclusive. Suppose P(X) = .05 and P(Y) = .02. What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?

4.) A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:
a. The probability of making exactly four sales.
b. The probability of making no sales.
c. The probability of making exactly two sales.
d. The mean number of sales in the two-hour period.

5.) In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

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