On page 45 and 46 of the etext, do question 65 parts a-d. here is the questibn 65. Movies A mathematician exploring the relationship between ratings of movies, their year of release, and their length discov- ered a paradox. Rather than list the data set of 100 movies in the original research, we have created a sample of size 10 that captures the properties of the original dataset. In the table below, the rating is a score from 1 to 10, and the length is in minutes. Source: Journal of Statistics Education. | | | Year Rating Length | Year Rating Length 2000 and the length. (b) Find the correlation coefficient between the length and the rating. E () Given that you found a positive correlation between the year and the length in part (a), and a positive correlation between the length and the rating in part (b), what would you expect about the correlation between the year and the rating? Calculate this correlation. Are you surprised? (115 8 Dilg il & 6 (a) Find the correlation coefficient between the years since S (d) Discuss the paradoxical result in part (c). Write what each correlation tells kuu. Try to explain what is happening. You may want to look at a scatterplot between the year and the rating, and consider which points on the scatterplot repre- sent movies of length no more than 110 minutes, and which represent movies of length 115 minutes or more. e