2. (4) Suppose that, for the coming year, the probability of a married man will buy a new phone is 0.21 the probability that a murried woman will buy a new plone is 0.28, and the probability that both the husband and wife will buy a new phone is 0.15. What is the probability that (1) at least one member of a married couple will buy a new phone next year? () a wife will buy a new phone next year, given that her husband will do? 1 mark) (iii) a bustand will buy a new phone next year, given that his wife will not? 11 mark) (b) A bank elueities borrowers as high-risk or low-risk. Only 20% of its kans are made to those in the high-risk category. Of all its loans, 10% are in default, and 35% of those in dubultare high-rink borrowe 6) What is the probability that a high-tk borrower will definult? 2 marks (H) What is the probability that a low-risk borrower will default? 13 mark (c) Acun the umber of twwly diagnosed cancer patients at Princess Margaret Hospital follows a Pobuson probability distribution. Based on past data, on average, 2 caiet patients are newly diagnosed at a hospital every day. 6) What is the probability there are less than a newly diagnosed canicor patients at Princess Margaret Hospital in a day 2 mark (W) What is the probability that there are less than 7 newly diagnosed cancer patients at Price Margaret Hospital in a week 2 marks () Compite the probability that in one month, there are at least 2 weeks in which there were la than 7 newly diagnosed cancer patients at Princess Margaret Hospital in those works. 3 mark) (1) The weights of bags of the processes at Bagorice company follow the normal distribution, with a moto of 9.20 pounds and a standard deviation of 0.25 pounds, The label Wright is given as 9.00 pour 6) Wluit proportion of the box of rice weighs be than the amount claimed on the label 1 mark) (1) Out of 20 bags of rice, what's the probability that more than 3 of them we below the amount claimed on the label? 2 marks (1) The Bay Rice company is considering two pans (A and B) to reduce the proportion of bugs of rice below label weight (Plan A) It can increase the toon weight at 9.25 pounds and leave the standard deviation in changed or (Plan B) It can leave the mean weight at 9.20 pounds and reduce the standard deviation from 0.25 pounds to 0.15 pounds. Which change (Plan A or Plan B) would you recotometid? 13 mars () The time it takes for a robot to semble a Honda car follow a formal distribution with mean 32 hours and a standard a standard deviation of 2 hours. Ideally, Honda manufacturers want the robots to sembile a Honda cax in less than 31 hour. Out of 500 radomly chce obrot, what's the probability that greater than 415 of the robots semble a car in ke than 34 hours? 14 mars 2. (4) Suppose that, for the coming year, the probability of a married man will buy a new phone is 0.21 the probability that a murried woman will buy a new plone is 0.28, and the probability that both the husband and wife will buy a new phone is 0.15. What is the probability that (1) at least one member of a married couple will buy a new phone next year? () a wife will buy a new phone next year, given that her husband will do? 1 mark) (iii) a bustand will buy a new phone next year, given that his wife will not? 11 mark) (b) A bank elueities borrowers as high-risk or low-risk. Only 20% of its kans are made to those in the high-risk category. Of all its loans, 10% are in default, and 35% of those in dubultare high-rink borrowe 6) What is the probability that a high-tk borrower will definult? 2 marks (H) What is the probability that a low-risk borrower will default? 13 mark (c) Acun the umber of twwly diagnosed cancer patients at Princess Margaret Hospital follows a Pobuson probability distribution. Based on past data, on average, 2 caiet patients are newly diagnosed at a hospital every day. 6) What is the probability there are less than a newly diagnosed canicor patients at Princess Margaret Hospital in a day 2 mark (W) What is the probability that there are less than 7 newly diagnosed cancer patients at Price Margaret Hospital in a week 2 marks () Compite the probability that in one month, there are at least 2 weeks in which there were la than 7 newly diagnosed cancer patients at Princess Margaret Hospital in those works. 3 mark) (1) The weights of bags of the processes at Bagorice company follow the normal distribution, with a moto of 9.20 pounds and a standard deviation of 0.25 pounds, The label Wright is given as 9.00 pour 6) Wluit proportion of the box of rice weighs be than the amount claimed on the label 1 mark) (1) Out of 20 bags of rice, what's the probability that more than 3 of them we below the amount claimed on the label? 2 marks (1) The Bay Rice company is considering two pans (A and B) to reduce the proportion of bugs of rice below label weight (Plan A) It can increase the toon weight at 9.25 pounds and leave the standard deviation in changed or (Plan B) It can leave the mean weight at 9.20 pounds and reduce the standard deviation from 0.25 pounds to 0.15 pounds. Which change (Plan A or Plan B) would you recotometid? 13 mars () The time it takes for a robot to semble a Honda car follow a formal distribution with mean 32 hours and a standard a standard deviation of 2 hours. Ideally, Honda manufacturers want the robots to sembile a Honda cax in less than 31 hour. Out of 500 radomly chce obrot, what's the probability that greater than 415 of the robots semble a car in ke than 34 hours? 14 mars