solve and show work respectively.. this was all the information given

Free Response Section You Must Show Your Work to Earn Full Credit 1. A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs. (20 points) # of repairs, x Probability, P(X = x) x - M ( x - 1) 2 ( x - M)2 . P (X = x) 0 0.80 1 0.11 0.05 W / N 0.04 Total [P(X = x ) =1 [(x - 1)2 . P(X = x) = a) Find the probability that no more than 2 repairs will be needed for these freezers. b) Find the expected (mean) number of repairs this kind of freezer is expected to need each year. Show your work. c) Find the variance and standard deviation of the number of repairs each year. Show your work.4. One cable company claims that it has excellent customer service. In fact, the company advertises that a technician will arrive within 30 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming that it takes over 30 minutes for the cable technician to arrive. The customer asks a simple random sample of 9 other cable customers how long it has taken the cable technician to arrive when they have called for one. The sample mean for this group is 33.2 minutes with a standard deviation of 3.4 minutes. Test the customer's claim at the 0.025 level of significance? (15 points) (a) State the null and alternate hypotheses. (b) Determine which distribution to use for the test statistic, and state the level of significance? (c) Calculate the test statistic. (d) Draw a conclusion and interpret the decision.5. A direct mail appeal for contributions from a university's alumni and supporters is considered cost effective if more than 15% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 250 people on the alumni and supporters mailing lists. He receives monetary contributions from 40 people. Does this evidence support the cost effectiveness of the direct mail appeal? Use a 0.05 level of significance. (15 points) (a) State the null and alternate hypothesis. (b) Determine which distribution to use for the test statistic. (c) Calculate the necessary sample test statistics (d) Draw a conclusion and interpret the decision