1. Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the u, the chance that he or she truly has the u (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the u, we are interested in how many actually have the u. (a) Dene the random variable and list its possible values. (b) State the distribution of X. (c) Find the probability that at least ve of the 25 patients actually have the u. (d) On average, for every 25 patients calling in, how many do you expect to have the u? 2. Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school. (a) In words, dene the random variable X. (b) List the values that X may take on. (c) Give the distribution of X, i.e., X ~ _(_,_) l (d How many seniors are expected to have participated in after-school sports all four years of high school? (e) Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically. (f) Based on numerical values, is it more likely that four or that ve of the seniors participated in after-school sports all four years of high school? Justify your answer numerically. Question 1. IfX represents the number of heads obtained in three tosses of a fair coin, (Create the table for both parts} {3) Find the probability distribution of X. (b) Find the expected value and the standard deviation. Question 2. A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year} festivities this year. Based on past years, she knows that 20% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. {3) Give the distribution ofX. X ~ ) {b} How many of the 12 students do we expect to attend the festivities? (_, {c} Find the probability that at most four students will attend. {d} Find the probability that more than two students will attend. {e} Find the standard deviation. Question 3. Suppose that about 80% of graduating students attend their graduation. A group of 25 graduating students is randomly chosen. {a} Give the distribution ofX. X ~ ) {b} How many are expected to attend their graduation? (_, {cl Find the probability that 18 students attend. {d} Find the standard deviation