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Question 1                                                                                                               (12)The table bellows shows the number of commuters using bus and train to travel to work by gender. Gender Bus commuters Train commuters Male 18 54 Female 59 20 If one commuter is randomly chosen, what is the probability the commuter is:1.1.1   male and use bus to travel to work?                                                                          1.1.2   using train to travel to work?                                                                                      1.1.3   female given that she use a bus to travel to work?                                                   1.2      Suppose event B and C are independent and not mutually exclusive, P (B) = 0.25 and P (C) = 0.39. Determine the following:1.2.1   P (B and C).                                                                                                               1.2.2   P (B or C).                                                                                                                  Question 2                                                                                                                            2.1      Fifteen athletes run a race. Two athletes are awarded prices for first and second positions. Determine the number of winning arrangements.                             2.2      Find the number of ways in which ten lecturers can be assigned to seven different courses. Assume that the lecturers are equally qualified.                                               Question 3                                                                                                                3.1      A study shows that 64% of students drop out in university due financial exclusions. From a random sample of 20 students, determine the probability that students dropping out in university due to financial exclusions is between 7 and 9. (Note: Binomial distribution).                                                                                             3.2      The probability that people will be placed on hold when they call a radio show with 3 phone line is 90%.                      3.2.1   Determine the expected value of the people who will be placed on hold.               3.2.2   Calculate the variance of the people who will be placed on hold.                 3.3       On average 5 children get infected with influenza per week. What is the probability that:3.3.1   less than 2 children will be infected with influenza in a random week?        3.3.2   exactly 4 children will be infected with influenza in one day?                       Question 4                                                                                                                The amount of the time a courier service company takes to deliver parcels to clients is normally distributed with a mean of 2 days and a standard deviation of 1 day. 4.1.1   What is the probability that a randomly selected parcel will take between 1 and 3 days to be delivered to the client?                                                                         4.1.2   What is the probability that a randomly selected parcel will take less than 2 days to be delivered to the clients?                                                                                               4.2      Suppose 10 parcels are randomly selected, what is the probability that the mean time of the parcels to be delivered to the clients is greater than 3 days?                     Question 5                                                                                                                5.1.1   A sample of 89 households is selected to assess whether they have access to water in their yard. 84 indicated that they had access to water in their yard. a) Calculate the standard error of the proportion.                                                                            b) If the population proportion is 85%           Find                                                                                                                     Math Statistics and Probability