Past statistics suggest that the "success rate" (survival rate five years after the transplant) of heart transplants about 75%. If one randomly selects ten patients who have just received a heart transplant, find the probabilit that all ten patients survive [2 marks] b. zero patients survive [2 marks] c. at most 4 patients survive [2 marks] d. more than 7 patients survive [2 marks] e. the majority of patients survive [2 marks] Problem 2. Lobster platter Over the past 50 supper evenings, a popular seafood restaurant has recorded the following data concerning d customer orders of its very expensive 2-pound fresh lobster dinner platter. X: Number of 2-pound fresh lobster dinner Frequency: platters ordered during the evening # of evenings 12 22 14 12 16 8 18 6 20 2 Total 80 50 Figure 1. Lobster dinner data. a. Let X be the number of 2-pound fresh lobster platters ordered by customers on any given evening. Construct a probability distribution for X, based on an analysis of the past 50 supper evenings, as described in the table above. Keep your calculations to two decimals. [5 marks] f. Based on the probability distribution constructed in part a above, compute the mean number of 2-pound fresh lobster platters ordered per evening. [2 marks]