Let the random variable x represent the number of automobiles thata top salesperson will sell to a corporate client. The only possible valuesfor x are 0, 1 and 2, and the possibilities for each of these values may becalculated from the formulap(x) = 0.5 – (x/6) where x = 0, 1 or 2.a. Construct the probability distribution of the variable xNOTE: Express your probabilities to 4 decimal places of accuracy.b. Calculate the mean of this probability distribution.c. Calculate the standard deviation of this probability distribution.d. What is the probability that a randomly selected top salespersonwill selli.At least 1 automobile to a corporate client ?iiAt most 1 automobile to a corporate client ?iiiExactly 1 automobile to a corporate client ?2. According to a recent study, 38% of all women will suffer a hipfracturebecause of osteoporosis by the age of 85. If six women aged 85 arerandomly selected, what is the probability thata. None of them will suffer (or has suffered) a hip fracture due toosteoporosis ?b. At least four of them will suffer (or have suffered) a hip fracture duetoOsteoporosis ?c. Fewer than two of them will suffer (or have suffered) a hip fracturedueto osteoporosis ?3. Seventy percent of the student body of a very large post secondaryinstitution is female. In a random sample of 12 students, what is theprobability thata. At most half will be females ?b. More that 7 will be females ?c. Fewer than 3 will be males ?