8:34AAsrPART ECollege Pro Paintingacrobat.adobe.comQYou have decided that for your summer job you are going to manage a group of students who willpaint houses to earn money for the summer. As Manager, your paycheck depends on yourcapability to efficiently schedule the team so that all the houses get painted on time with little, orideally no, overage on scheduled man-hours.Given that a house requires H man-hours to paint, your team has N houses to paint and S studentson the team:Ⓒi. Write the expression that relates the number of students that you will need to schedule to finishpainting the houses in 12 weeks assuming 40-hour work weeks.0ii. If it takes 120 man-hours to paint a house and your team has 36 houses to paint, how manystudents do you need to hire to paint the houses in 12 weeks assuming 40-hour workweeks?2iii. A friend of yours, Bionka, managed a College Pro Painting team last summer and tells youthat since every student is not as efficient as you may expect combined with the fact that theneighborhood you're covering has both small and large houses, the number of man-hours to painta house, H, is not exactly 120. Instead, she tells you that H is equally likely to take anywhere from110 man-hours to 140 man-hours. Additionally, Bionka hints that not all of your workers showup as expected. In fact, during a given week a man-day (8 hours) of work is lost on the average of1.1 times. Fill in the following probability tables:110 120HP(H)130Let R = Number of times 8 man-hours (a man-day) will be lost in a weekR134P(R)☎140105Recall that you have 12 weeks to paint these houses. Considering the two 'risks of uncertaintycharacterized by the above tables that contain more realistic information regarding the number ofman-hours that will probably be required to paint the 36 houses and the number of man-days ofwork that will probably be lost per week for each of the 12 weeks, how many students should yourecruit to be most efficient? Briefly explain your answer.8PROBLEM-SOLVING DELIVERABLESYou should work in teams of either two or three. You may not work alone. Turn in your resultsfor Parts A, B, C, D, and E and your team's signed cover page at the beginning of your team'slecture on Monday, October 2, 2023 for Professor Siadat's lecture or Tuesday, October 3, 2023for Professor Hanna's lecture. One set of results should be submitted per team.2 PART ARoll a single standard six-sided die 36 times and tabulate your results (i.e., number of 1's, numberof 2's,..., number of 6's). Calculate the mean, variance and standard deviation of your data.PART BRoll a pair of standard six-sided dice 36 times and tabulate your results (i.e., number of 2's, numberof 3's,..., number of 12's). Calculate the mean, variance and standard deviation of your data.PART CSuppose you have a pair of six-sided dice where each die contains the following sides:(1, 2, 2, 4, 5, 5). In theory, if you rolled this pair of dice 36 times, how many times would youobtain a total of 2, 3, 4, 5, 6, 7, 8, 9 and 10? Using graph paper, plot the distribution of expectedvalues. Calculate the mean, variance, and standard deviation of this distribution.PART DThe number of false fire alarms in a suburb of Detroit averages 7.6 per day. Assuming that aPoisson distribution is appropriate:What is the probability that exactly 7 false alarms will occur on a given day?What is the probability that less than 7 false alarms will occur on a given day?What is the probability that more than 7 false alarms will occur on a given day?(Hint: the probabilities of all possible cases must add to one).1

PART A Roll a single standard six-sided die 36 times and tabulate your results (i.e., number of 1's, number of 2's, ..., number of 6's). Calculate the mean, variance and standard deviation of your data. PART B Roll a pair of standard six-sided dice 36 times and tabulate your results (i.e., number of 2's, number of 3's,..., number of 12's). Calculate the mean, variance and standard deviation of your data. PART C Suppose you have a pair of six-sided dice where each die contains the following sides: (1, 2, 2, 4, 5, 5). In theory, if you rolled this pair of dice 36 times, how many times would you obtain a total of 2, 3, 4, 5, 6, 7, 8, 9 and 10? Using graph paper, plot the distribution of expected values. Calculate the mean, variance, and standard deviation of this distribution. PART D The number of false fire alarms in a suburb of Detroit averages 7.6 per day. Assuming that a Poisson distribution is appropriate: What is the probability that exactly 7 false alarms will occur on a given day? What is the probability that less than 7 false alarms will occur on a given day? What is the probability that more than 7 false alarms will occur on a given day? (Hint: the probabilities of all possible cases must add to one). 1