2. a) A report from the Secretary of Health and Human Services stated that 60% of single vehicle traffic fatalities that occur at night on the weekend involve an intoxicated driver. Consider a random sample of 12 single vehicle traffic fatalities that occured at night on a weekend. Let X denote the number of fatalities in the sample involving an intoxicated driver. We can represent the distribution for X as X~B(n,p). i) Determine the values of n and p which define the distribution for X. n p = Determine the probability that the number of fatalities involving an intoxicated driver will be (correct to 4 decimal places): ii) Equal to 6 Prob = iii) More than 5 Prob= iv) At least 3 and at most 6 Prob [5 marks] b) The small life insurance company has determined that on average it receives 1 claims per day. Let X denote the number of claims receive by the company in a day. We can represent the distribution of X as X-Poi(). i) Determine the value of u which defines the distribution for X. Determine the probability that the number of claims in a day is (correct to 4 decimal places): ii) Equal to 3 Prob = Determine the probability that the number of claims in a day is (correct to 4 decimal places): ii) Equal to 3 Prob iii) Less than 2 Prob Let Y denote the number of claims received in a two day period. We can represent the distribution for Y as Y~Poi(u). iv) Determine the value of u whcih defined the distribution for Y. Determine the probability that the number of claims in two days is (correct to 4 decimal places): v) At least 6 Prob [5 morkal