Input Analysis question

Question 1: Using a priori knowledge of standard distributions for each of the following cases specify a distribution. Importantly, justify your answer. 1. Customers arrive to a system one at a time, the arrivals are inde- pendent, are highly variable and the arrivals occur at a constant rate. 2. A person's job is to install 98 rivets in the right wing of an airplane under construction. If the random variable 7 is the total time re- quired for one airplane, then what is the approximate distribution of T? 3. A crate of parts which contains 20 parts are tested independently. The probability that a part passes the test has been calculated to be 0.02. In a simulation model, it is required to sample from a distribution that will give the number of parts that pass the test from one crate. 16% Question 2: As part of obtaining surgery porters are available to escort patients to pre-surgery preparation area. Patients are not allowed to go by themselves as a matter of policy. A consultant hired to develop a simulation model walked the route briskly and found it took 2 minutes to walk to the prep area. Porters say that it sometimes takes as long as 7 minutes to escort a patient to the area, but it usually takes 5 minutes. Construct a beta distribution model for time to escort a patient based on the information given.Table 1: Data for Question 4. 88.3 40.7 36.3 27.3 36.8 91.7 67.3 7.0 45.2 23.3 98.8 90.1 17.2 23.7 97.4 32.4 87.8 69.8 62.6 99.7 20.6 73.1 21.6 6.0 45.3 76.6 73.2 27.3 87.6 87.2 16% Question 3: Use the chi-squared test to ascertain that the following num- bers come from the uniform distribution with lower value equal to 0 and upper value equal to 1: 0.594, 0.928, 0.515, 0.055, 0.507, 0.351, 0.262, 0.797, 0.788, 0.442, 0.097, 0.798, 0.227, 0.127, 0.474, 0.825, 0.007, 0.182, 0.929, 0.852. 16% Question 4: It is surmised that the data on the incidence of accidents for a month along a road in Table 1 may follow the uniform distribution. Use the Kolmogorov-Smirnov test to discover whether the distribution of location of accidents is uniformly distributed. 16% Question 5: Outline the procedure for fitting a continuous random variable to a standard distribution. To obtain additional marks use citations outside your module notes