Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information on misorientation angle (degrees) was extracted from the article “Observations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy: Crystallographic Orientation and Size Effects (Metallurgical and Materials Trans., 2006: 1507–1518). a. Is it true that more than 50% of the sampled angles are smaller than 15°, as asserted in the paper? b. What proportion of the sampled angles are at least 30°? c. Roughly what proportion of angles are between 10° and 25°? d. Construct a histogram and comment on any interesting features.

Answer: Step1: The given information on misorientation angle (degrees) was extracted from the article “Observations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy: Crystallographic Orientation and Size Effects (Metallurgical and Materials Trans., 2006: 1507–1518). Class Relative frequency 0-5 0.177 5-10 0.166 10-15 0.175 15-20 0.136 20-30 0.194 30-40 0.078 40-60 0.044 60-90 0.030 Step2: a). The aim is, is it true that more than 50% of the sampled angles are smaller than 15°, as asserted in the paper For the first three classes to determine the proportion of angles that are smaller than 15°. Proportion of angles smaller than 15° = relative frequency for 0-5 + relative frequency 5-10 + relative frequency 10-15. = 0.177 + 0.166 + 0.175 = 0.518. Therefore, the proportion of angles that are smaller than 15° is 0.518 is greater than 0.5. So the...