1. The problem asks to compare the mean movie lengths of Jacob's and Ayumi's favorite actors. 2. The mean (average) is calculated by summing all the movie lengths and dividing by the number of movies. 3. Jacob's movie lengths are: 105, 107, 117, 115, 98, 103, 99, 99, 105, 112, 112, 109. 4. Sum Jacob's lengths: $$105 + 107 + 117 + 115 + 98 + 103 + 99 + 99 + 105 + 112 + 112 + 109 = 1281$$ 5. Count Jacob's movies: 12. 6. Calculate Jacob's mean: $$\text{mean}_J = \frac{1281}{12}$$ 7. Simplify with cancellation: $$\frac{\cancel{1281}}{\cancel{12}} = 106.75$$ 8. Ayumi's movie lengths are: 97, 101, 110, 97, 114, 96, 114, 109, 103, 97. 9. Sum Ayumi's lengths: $$97 + 101 + 110 + 97 + 114 + 96 + 114 + 109 + 103 + 97 = 1038$$ 10. Count Ayumi's movies: 10. 11. Calculate Ayumi's mean: $$\text{mean}_A = \frac{1038}{10}$$ 12. Simplify: $$\frac{\cancel{1038}}{\cancel{10}} = 103.8$$ 13. Compare means: Jacob's mean is $106.75$ min, Ayumi's mean is $103.8$ min. 14. Conclusion: The movies from Jacob's favorite actor are longer since their mean, $106.75$ min, is greater than the mean length of movies from Ayumi's favorite actor, $103.8$ min.