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WebAssign for Devore's Probability and Statistics for Engineering and the Sciences, 9th Edition [Instant Access], Single-Term
9th Edition
ISBN: 9780357893104
Author: Devore; Jay L.
Publisher: Cengage Learning US
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Textbook Question
Chapter 12.1, Problem 1E
The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).
| Temp. | 170 | 172 | 173 | 174 | 174 | 175 | 176 |
| Ratio | .84 | 1.31 | 1.42 | 1.03 | 1.07 | 1.08 | 1.04 |
| Temp. | 177 | 180 | 180 | 180 | 180 | 180 | 181 |
| Ratio | 11.80 | 1.45 | 1.60 | 1.61 | 2.13 | 2.15 | .84 |
| Temp. | 181 | 182 | 182 | 182 | 182 | 184 | 184 |
| Ratio | 11.43 | .90 | 1.81 | 1.94 | 2.68 | 1.49 | 2.52 |
| Temp. | 185 | 186 | 188 |
| Ratio | 13.00 | 1.87 | 3.08 |
- a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.
- b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.
- c. Construct a
scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.
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West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
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Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
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Months
Unemployed
Number
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1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 12 Solutions
WebAssign for Devore's Probability and Statistics for Engineering and the Sciences, 9th Edition [Instant Access], Single-Term
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