8) (15 Points) We collected 200 data to understand the automobiles' time between arrivals to the Guy and St-Catherine streets intersection. We found that, the average time between arrivals is 5.25 minutes with a standard deviation of 3 minutes. We also know that minimum time between arrivals is 0 minutes, median is 12 minutes and the maximum is 25 minutes. Also we constructed the following histogram to better understand the distribution of our data. 40 30 25 201 15 10 5 8 10 12 14 16 18 20 22 Furthermore, in order to prove the data is triangularly distributed, following goodness-of-fit test is performed. Fill out the empty parts in the table and conclude if the data is distributed triangularly distributed (probability density function for the triangular distribution is provided below) using 80% confidence level (alpha = 0.20) Interval Expected Expected Chi- Min Max Observations Probability Frequency Square Expected Expected Chi- Number of Min Max Number of Observations Probability Frequency Square 0 2 3 0.013 2.67 0.042 2 4 5 0.040 8.00 1.125 4 6 5 0.067 13.33 5.208 6 8 12 0.093 18.67 2.381 8 10 34 0.120 24.00 4.167 10 12 22 ? ? ? 12 14 33 0.148 29.54 0.406 14 16 35 0.123 24.62 4.381 16 18 16 0.098 19.69 0.692 18 20 15 0.074 14.77 0.004 20 22 12 0.049 9.85 0.471 22 25 8 0.028 5.54 1.094 Total 200.000 1.000 200.000 ? 2(x-a) (b-a)(c-a) a x c f(x)= 2(b-x) c x b (b-a)(b-c)