16   Question 4 continued The wind farm has six wind turbines. During the past five years, there have been 84 wind turbine failures at the wind farm. (g) Show how Petra used this information to calculate the value of λ (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (h) Make three criticisms, in context, of Petra’s use of a Poisson model with  λ = 2.8  for the number of failures per year for each wind turbine. You may consider both the use of a Poisson model and the value of λ (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 4 is 14 marks) Turn over 17   5 Dennis and Viola are doing a course in film studies. They want to conduct a study into the factors affecting film running times. They start by investigating the distribution of film running times. Dennis and Viola extract a random sample of 250 films from a database containing the names and dates of all films ever made and look up the running time of each film in their sample on the internet. They use graphing software to produce a histogram of their results, shown in Figure 5. 60 80 100 120 140 160 180 200 Frequency Film running time (minutes) 70 60 50 40 30 20 10 0 [Data sources: www.cinemetrics.lv, www.imdb.com] Figure 5 Viola believes that a normal distribution might be a suitable model for film running times. (a) Explain one feature of Figure 5 that supports Viola’s belief. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (b) Explain one feature of Figure 5 that does not support Viola’s belief. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________