Twelve jurors are randomly selected from a population of 4 million residents. Of these 4 million residents, it is known that 45% are of a minority race. Of the 12 jurors selected, 2 are minorities.(a) What proportion of the jury described is from a minority race?(b) If 12 jurors are randomly selected from a population where 45% are minorities, what is the probability that 2 or fewer jurors will be minorities?(c) What might the lawyer of a defendant from this minority race argue?.....(a) The proportion of the jury described that is from a minority race is(Round to two decimal places as needed.)(b) The probability that 2 or fewer out of 12 jurors are minorities, assuming that the proportion of the population that are minorities is 45%, is(Round to four decimal places as needed.)(c) Choose the correct answer below.O A. The number of minorities on the jury is impossible, given the composition of the population from which it came.B. The number of minorities on the jury is reasonable, given the composition of the population from which it came.OC. The number of minorities on the jury is unusually high, given the composition of the population from which it came.D. The number of minorities on the jury is unusually low, given the composition of the population from which it came.StatcrunchNext7:59SAMSUNGesc232$%&1234backspace78tabeV个 Suppose a life insurance company sells a $160,000 1-year term life insurance policy to a 20-year-old female for $320. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is0.999544. Compute and interpret the expected value of this policy to the insurance company.The expected value is(Round to the nearest cent as needed.)Which of the following interpretations of the expected value is correct? Select the correct choice below and fill in the answer box to complete your choice.(Round to the nearest cent as needed.)O A. The insurance company expects to make a profit of $on every 20-year-old female it insures for 1 month.O B. The insurance company expects to make a minimum profit of $on every 20-year-old female it insures for 1 month.O C. The insurance company expects to make a profit of $on every 20-year-old female it insures for 1 year.O D. The insurance company expects to make a maximum profit of $on every 20-year-old female it insures for 1 year.StatcrunchNextO 7:59esc@232$&backspace13478uの口 5

"Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question." Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials being independent and the probability of success, say p, remaining constant, then the distribution of the number of success follows binomial. Let us assume X be a random variable denoting the number of success. Then X~bin(n, p), n and p being the parameters of the binomial distribution. The probability mass function of X is given by,We have, the total number of jurors is 12. And the number of jurors that are from minority race is 2. Therefore, the proportion of the jury that are from minority race is: 212×100%=16.67 (rounded to 2 decimal places). Answer: The blank will be filled up with 16.67%.Let us assume X is a random variable denoting the number of jurors that are minorities out of 12 jurors. We have, the probability that a randomly selected jury member is minority is 45%=0.45. Here, i) all the jurors are independent ii) for each juror, there are two possibilities - the juror is from minority (success) or not (failure) iii) the probability of a juror being from minority race remains constant for all the jurors Under these conditions we can say that, X~bin(n, p) with Therefore, the probability that 2 or fewer jurors will be minorities is Answer: The blank will be filled up with 0.0421.From the above solution (a), we have the proportion of minorities among the 12 selected jurors is 16.67% whereas in the population the proportion is 45%. From solution (b), the probability that 2 or fewer jurors are from minority race is 0.0421 which is a very small probability. Under these two results, we can conclude that the number of minorities on the jury is unusually low. Answer: The correct answer is: Option D. Therefore, all other options are incorrect.