Solution Found!
Answer: The accompanying frequency distribution of
Chapter 1, Problem 65E(choose chapter or problem)
Problem 65E
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:
Problem 65E
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 |
Frequency |
Relative 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).