18   Question 5 continued Dennis and Viola agree that they should perform a goodness‑of‑fit test to investigate whether a normal distribution would be a suitable model for film running times. For their sample of 250 films, the mean running time is 105.26 minutes and the standard deviation of the running times is 22.18 minutes. Part of their working is shown in Figure 6. Film running time (minutes) Observed frequency Probability (4 d.p.) Expected frequency (2 d.p.) x  60 4 0.0206 5.16 60 < x  80 22 0.1067 26.68 80 < x  100 90 s u 100 < x  120 85 t v 120 < x  140 32 0.1945 48.63 140 < x  160 11 0.0518 12.96 x > 160 6 0.0068 1.70 Total 250 1 250 Figure 6 (c) Find the values of s, t, u and v missing from Figure 6. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 19   Question 5 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (d) Explain, with a reason, what adjustment Viola and Dennis must make to the data in Figure 6 before they can carry out the χ2 goodness-of-fit test. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________