Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 11.9, Problem 87E
a.
To determine
Find the transformation for generating the linear model if the given
b.
To determine
Find the transformation for generating the linear model if the given function is an intrinsically linear function.
c.
To determine
Find the transformation for generating the linear model if the given function is an intrinsically linear function.
d.
To determine
Find the transformation for generating the linear model if the given function is an intrinsically linear function.
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
From a sample of 26 graduate students, the mean number of months of work experience prior to entering an MBA program was 34.67. The national standard deviation is known to be18 months. What is a 90% confidence interval for the population mean?
Question content area bottom
Part 1
A
9090%
confidence interval for the population mean is
left bracket nothing comma nothing right bracketenter your response here,enter your response here.
(Use ascending order. Round to two decimal places as needed.)
A test consists of 10 questions made of 5 answers with only one correct answer. To pass the test, a student must answer at least 8 questions correctly. (a) If a student guesses on each question, what is the probability that the student passes the test? (b) Find the mean and standard deviation of the number of correct answers. (c) Is it unusual for a student to pass the test by guessing? Explain.
Chapter 11 Solutions
Applied Statistics and Probability for Engineers
Ch. 11.2 - 11-1. Diabetes and obesity are serious health...Ch. 11.2 - 11-2. On average, do people gain weight as they...Ch. 11.2 - Prob. 3ECh. 11.2 - 11-4. Regression methods were used to analyze the...Ch. 11.2 - 11-5. See Table E11-1 for data on the ratings of...Ch. 11.2 - 11-6. An article in Technometrics by S. C. Narula...Ch. 11.2 - 11-7. The number of pounds of steam used per month...Ch. 11.2 - 11-8. Go Tutorial Table E11-3 presents the highway...Ch. 11.2 - Prob. 9ECh. 11.2 - 11-10. An article in the Journal of Sound and...
Ch. 11.2 - Prob. 11ECh. 11.2 - 11-12. An article in the Journal of Environmental...Ch. 11.2 - 11-13. A rocket motor is manufactured by bonding...Ch. 11.2 - 11-14. Go Tutorial An article in the Journal of...Ch. 11.2 - 11-15 An article in the Journal of the...Ch. 11.2 - 11-16. An article in Wood Science and Technology...Ch. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - 11-20. Show that in a simple linear regression...Ch. 11.2 - 11-21. Consider the simple linear regression model...Ch. 11.2 - 11-22. Suppose that we wish to fit a regression...Ch. 11.4 - 11-23. Recall the regression of percent body fat...Ch. 11.4 - Prob. 24ECh. 11.4 - 11-25. Suppose that in Exercise 11-24 weight is...Ch. 11.4 - 11-26. Consider the simple linear regression model...Ch. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - 11-31. Consider the National Football League data...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - 11-35. Consider the data from Exercise 11-9 on y =...Ch. 11.4 - Prob. 36ECh. 11.4 - 11-37. Consider the data from Exercise 11-13, on y...Ch. 11.4 - 11-38. Consider the data from Exercise 11-12 on y...Ch. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 44ECh. 11.6 - 11-45. Using the regression from Exercise...Ch. 11.6 - 11-46. Q Using the regression from Exercise...Ch. 11.6 - 11-47. Refer to the data in Exercise 11-3 on y =...Ch. 11.6 - 1-48. Exercise 11-4 presented data on roadway...Ch. 11.6 - 11-49. Refer to the NFL quarterback ratings data...Ch. 11.6 - Prob. 50ECh. 11.6 - 11-51. Exercise 11-7 presented data on y = steam...Ch. 11.6 - 11-52. Exercise 11-8 presented gasoline mileage...Ch. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - 11-56. Exercise 11-12 presented data on chloride...Ch. 11.6 - 11-57. Refer to the data in Exercise 11-13 on...Ch. 11.6 - Prob. 58ECh. 11.6 - Prob. 59ECh. 11.7 - 11-60. Consider the simple linear regression model...Ch. 11.7 - 11-61. Repeat Exercise 11-60 using an error term...Ch. 11.7 - 11-62. Refer to the compressive strength data in...Ch. 11.7 - 11-63. Refer to the NFL quarterback ratings data...Ch. 11.7 - 11-64. Refer to the data in Exercise 11-6 on...Ch. 11.7 - 11-65. Refer to the data in Exercise 11-7 on y =...Ch. 11.7 - 11-66. Refer to the gasoline mileage data in...Ch. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - 11-69. Refer to Exercise 11-12. which presented...Ch. 11.7 - Prob. 70ECh. 11.7 - 11-71. Consider the rocket propellant data in...Ch. 11.7 - 11-72. Consider the data in Exercise 11-9 on y =...Ch. 11.7 - Prob. 73ECh. 11.7 - Prob. 74ECh. 11.7 - Prob. 75ECh. 11.8 - 11-76. Suppose that data are obtained from 20...Ch. 11.8 - 11-77. Suppose that data are obtained from 20...Ch. 11.8 - Prob. 78ECh. 11.8 - 11-79. A random sample of 50 observations was made...Ch. 11.8 - 11-80. The data in Table E11-6 gave x = the water...Ch. 11.8 - Prob. 81ECh. 11.8 - 11-82. The weight and systolic blood pressure of...Ch. 11.8 - Prob. 83ECh. 11.8 - Prob. 84ECh. 11.8 - 11-85. Refer to the NFL quarterback ratings data...Ch. 11.8 - Prob. 86ECh. 11.9 - Prob. 87ECh. 11.9 - Prob. 88ECh. 11.9 - 11-89. An electric utility is interested in...Ch. 11.10 - Prob. 90ECh. 11.10 - 11-91. The compressive strength of an alloy...Ch. 11.10 - Prob. 92ECh. 11.10 - Prob. 93ECh. 11.10 - Prob. 94ECh. 11.10 - 11-95 Consider the propellant data is Exercise...Ch. 11 - Prob. 96SECh. 11 - Prob. 97SECh. 11 - 11-98. The strength of paper used in the...Ch. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 101SECh. 11 - Prob. 102SECh. 11 - 11-103. An article in the Journal of Applied...Ch. 11 - 11-104. Two different methods can be used for...Ch. 11 - 11-105. The grams of solids removed from a...Ch. 11 - Prob. 106SECh. 11 - 11-107. The data in Table E11-20 related diamond...Ch. 11 - Prob. 108SECh. 11 - Prob. 109SECh. 11 - Prob. 110SECh. 11 - 11-111. Consider the simple linear regression...Ch. 11 - Prob. 112SECh. 11 - Prob. 113SECh. 11 - Prob. 114SECh. 11 - Prob. 115SECh. 11 - Prob. 116SE
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