Question

PPetrol is restructuring its distribution network of gas stations. In particular, it has to decide on the number of petrol pumps to install at gas stations in proximity of hyper- and supermarkets. The interarrival times (in minutes) of clients at such gas stations are the following: 0.2 1.2 0.8 0.1 0.7 1.5 1.4 0.2 0.3 0.5 0.4 1.0 0.9 3.2 0.9 1.4 1.7 1.2 0.8 0.5 2.0 1.3 0.5 3.6 0.7 1.5 1.2 3.2 1.3 0.5

The sample standard deviation is 0.88.

a. Which is the most suitable probability distribution to represent the data? Justify your answer. [15 marks] b. Using an appropriate test, check that the observed data are compatible with the probability distribution identified in part (a) above. [35 marks]

c. Compute a 95% confidence interval for the expected value of interarrival times and provide the rationale of your answer. [25 marks]

d. What is the probability that at most one client will arrive in the next 5 minutes? Justify your answer. [20 marks]

e. Suppose that clients stay at the gas station for 5 minutes, how many petrol pumps does PPetrol need to install to guarantee an average utilization of the pumps of 60%? [10 marks]

Answer 1