Problem 3 12 points] r-1.5x7 3 The repair time (in hours) for an industrial machine has agamma distribution with mean 1.5 and variance 0.75. 1- Determine the probability that a repair time exceeds 2 hours, p(x-2)=1-p(x<2) λ=2 from r=3 table 10.75 2/1.5 25 =1-0.3233 = 0.6767 The No. 75 186.75 1.52-0.75& 1.5/2 = 10.866022) 6.47735 2- Determine the probability that a repair time is at least 5 hours given that it already exceeds 2 hours. P(x<5)-0.8753 from table Problem 4 12 points] A school employs 75 teachers. The following table summarises their length of service et the school, classified by gender. Less than 3 years 3 years to 8 years More than 8 years Female 12 20 13 45 Male 8 15 7 20 275 a- Find the probability that a randomly selected teacher: (i)- is female; 20 13 + = 0.6 75 12 +25 P (F) = 1 + (ii)- is female, given that the teacher has more than 8 years service; P(F/ more more than 8) P(F) = P(more than 81F).P(more than more than's more than 8) (13/75)x(20/75) 0.07703 х (iii)- is female, given that the teacher has less than 3 years service. P(F/less than 3) =P (less than 3/F). P (less than 3) 2 (12/75) x (20/15) 455 P(F) 0.07111 b- Are the event of selecting a female teacher and the event of selecting a teacher with less than 3 years service independent? Explain. Yes x Problem 512 points] Mr. Willis goes to school five days a week. On any given day, the probability that he goes on an orange bus is 0.3 a) Write down the expected number of days that Mr. Willis goes to work at his school on an orange bus in one week P(x=-5)= e-s 5! P(0)=0.3 5days a week " 0.175 46 In one week, find the probability that he goes to work on an orange bus b) on exactly three days P(x-3)= e-s 5³ = 0.14037 3! c) on at least two days. P(x>2) = 1- P(X ≤1) = 1-0-0404 =0.9596