Solution Found!
The accompanying frequency distribution of fracture
Chapter 2, Problem 65E(choose chapter or problem)
The accompanying frequency distribution of fracture strength (MPa) observations for ceramic bars fired in a particular kiln appeared in the article “Evaluating Tunnel Kiln Performance” (?Amer. Ceramic Soc. Bull., ?Aug. 1997: 59–63). a?. ?Construct a histogram based on relative frequencies, and comment on any interesting features. b.? ?What proportion of the strength observations are at least 85? Less than 95? c. Roughly what proportion of the observations are less than 90?
Questions & Answers
QUESTION:
The accompanying frequency distribution of fracture strength (MPa) observations for ceramic bars fired in a particular kiln appeared in the article “Evaluating Tunnel Kiln Performance” (?Amer. Ceramic Soc. Bull., ?Aug. 1997: 59–63). a?. ?Construct a histogram based on relative frequencies, and comment on any interesting features. b.? ?What proportion of the strength observations are at least 85? Less than 95? c. Roughly what proportion of the observations are less than 90?
ANSWER:Answer: Step 1 of 3 a. We need to construct a histogram based on relative frequencies Class Frequenc Relative y frequency 81 - <83 6 0.035502959 83 - <85 7 0.041420118 85 - <87 17 0.100591716 87 - <89 30 0.177514793 89 - <91 43 0.25443787 91 - <93 28 0.165680473 93 - <95 22 0.130177515 95 - <97 13 0.076923077 97 - <99 3 0.017751479 Sum 169 1 The histogram appears below. A representative value for this data would be around 90 MPa. The histogram is reasonably symmetric, unimodal, and somewhat bell-shaped with a fair amount of variability (s 3 or 4 MPa).