business statitstics

i want the following two question to be sloved by thrusday morning.. Question 5 4 Marks (a) An operator for a telephone-answering service answers a large number of calls for two real estate agents. The two agents are charged the same monthly fee for this service and it is assumed that they will each receive approximately half the calls coming in. Based on this assumption, find the probability that in the next 150 calls 90 or more will be for one agent. (Use normal approximation of the binomial distribution.) 1 mark (b) It is found that 60% of Australians who exercise daily by walking are women. A randomly selected group comprises of 15 people who exercise daily, with certain number of women in the group. What is the approximate probability that there will be an exactly 11 females in the group? 1.5 marks (c) A survey of 500 engineers found that 60 of them indicated that they were unhappy with their present work environment. A similar study conducted 3 years ago found that 8% of engineers were unhappy. The following hypotheses were established: Ho : p = 0.08 H1 : p ≠ 0.08 After completion of the hypothesis testing analysis, the p-value is found to be 0.00096. Using this p-value and a 1% level of significance, state whether the null hypothesis should or should not be rejected. Briefly explain why or why not. 1.5 marks (a) The payments for hospital bills at the local hospital are either private payments (made by patients) or third-party payments made by insurance companies. The payments made at the hospital are divided between private and third-party in such a way that the probability of a third-party payment is 0.75. Two-thirds of those third-party payments are for surgical bills, and one-third is for non-surgical bills. The private payments, however, are split 50-50 between payments for surgery and non-surgery items. (i) Find the probability that a randomly selected payment is both private and for a surgical item. 1 mark (ii) Find the probability that a randomly selected payment both is third-party and does not involve a surgical item. 1 mark (iii) What is the probability that a randomly selected payment is for a surgical item? 1 mark (b) CQUniversity is inviting a delegation of three (3) students to a convention being held at Rockhampton campus. It is indicated that only one (1) person will be selected from each of the three schools: business, engineering, and arts. There are four (4) business, six (6) engineering, and three (3) arts students who are eligible to attend the convention. How many different delegations could CQUniversity invite to the convention? i want this sums to be sloved with formula and calculation should be show