Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.2, Problem 22E
According to the article “Modeling and Predicting the Effects of Submerged Arc Weldment Process Parameters on Weldment Characteristics and Shape Profiles” (J. of Engr. Manuf., 2012: 1230–1240), the submerged arc welding (SAW) process is commonly used for joining thick plates and pipes. The heat affected zone (HAZ), a band created within the base metal during welding, was of particular interest to the investigators. Here are observations on depth (mm) of the HAZ both when the current setting was high and when it was lower.
| Non-high | 1.04 | 1.15 | 1.23 | 1.69 | 1.92 |
| 1.98 | 2.36 | 2.49 | 2.72 | ||
| 1.37 | 1.43 | 1.57 | 1.71 | 1.94 | |
| 2.06 | 2.55 | 2.64 | 2.82 | ||
| High | 1.55 | 2.02 | 2.02 | 2.05 | 2.35 |
| 2.57 | 2.93 | 2.94 | 2.97 |
a. Construct a comparative boxplot and comment on interesting features.
b. Is it reasonable to use the two-sample t test to test hypotheses about the difference between true average HAZ depths for the two conditions?
c. Does it appear that true average HAZ depth is larger for the higher current condition than for the lower condition? Carry out a test of appropriate hypotheses using a significance level of .01.
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GISS
Worksheet 10
Jesse runs a small business selling and delivering mealie meal to the spaza shops.
He charges a fixed rate of R80, 00 for delivery and then R15, 50 for each packet of
mealle meal he delivers. The table below helps him to calculate what to charge
his customers.
10
20
30
40
50
Packets of mealie
meal (m)
Total costs in Rands
80
235
390
545
700
855
(c)
10.1.
Define the following terms:
10.1.1. Independent Variables
10.1.2. Dependent Variables
10.2.
10.3.
10.4.
10.5.
Determine the independent and dependent variables.
Are the variables in this scenario discrete or continuous values? Explain
What shape do you expect the graph to be? Why?
Draw a graph on the graph provided to represent the information in the
table above.
TOTAL COST OF PACKETS OF MEALIE MEAL
900
800
700
600
COST (R)
500
400
300
200
100
0
10
20
30
40
60
NUMBER OF PACKETS OF MEALIE MEAL
Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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