6   3. During the summer, mountain rescue team A receives calls for help randomly with a rate of 0.4 per day. (a) Find the probability that during the summer, mountain rescue team A receives at least 19 calls for help in 28 randomly selected days. (2) The leader of mountain rescue team A randomly selects 250 summer days from the last few years. She records the number of calls for help received on each of these days. (b) Using a Poisson approximation, estimate the probability of the leader finding at least 20 of these days when more than 1 call for help was received by mountain rescue team A. (4) Mountain rescue team A believes that the number of calls for help per day is lower in the winter than in the summer. The number of calls for help received in 42 randomly selected winter days is 8 (c) Use a suitable test, at the 5% level of significance, to assess whether or not there is evidence that the number of calls for help per day is lower in the winter than in the summer. State your hypotheses clearly. (4) During the summer, mountain rescue team B receives calls for help randomly with a rate of 0.2 per day, independently of calls to mountain rescue team A. The random variable C is the total number of calls for help received by mountain rescue teams A and B during a period of n days in the summer. On a Monday in the summer, mountain rescue teams A and B each receive a call for help. Given that over the next n days P(C = 0) < 0.001 (d) calculate the minimum value of n (3) (e) Write down an assumption that needs to be made for the model to be appropriate. 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