Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 8, Problem 114SE
To determine
Prove that the length of the interval L is minimized when
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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.
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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.
Chapter 8 Solutions
Applied Statistics and Probability for Engineers
Ch. 8.1 - 8-1. For a normal population with known variance...Ch. 8.1 - 8-2. For a normal population with known variance...Ch. 8.1 - 8-3. Consider the one-sided confidence interval...Ch. 8.1 - 8-4. A confidence interval estimate is desired for...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - 8-8. Following are two confidence interval...Ch. 8.1 - 8-9. Suppose that n = 100 random samples of water...Ch. 8.1 - 8-10. Past experience has indicated that the...
Ch. 8.1 - 8-11. The yield of a chemical process is being...Ch. 8.1 - 8-12. The diameter of holes for a cable harness is...Ch. 8.1 - 8-13. A manufacturer produces piston rings for an...Ch. 8.1 - 8-14. The life in hours of a 75-watt light bulb is...Ch. 8.1 - 8-15. A civil engineer is analyzing the...Ch. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - 8-20. If the sample size n is doubled, by how much...Ch. 8.1 - 8-21. Go Tutorial An article in the Journal of...Ch. 8.1 - 8-22. Ishikawa et al. (Journal of Bioscience and...Ch. 8.1 - Prob. 23ECh. 8.2 - 8-24. Find the values of the following...Ch. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - 8-27. A random sample has been taken from a normal...Ch. 8.2 - 8-28. A random sample has been taken from a normal...Ch. 8.2 - 8-29. A research engineer for a tire manufacturer...Ch. 8.2 - 8-30. An Izod impact test was performed on 20...Ch. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - 8-34. An article in the Journal of Composite...Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - 8-38. A particular brand of diet margarine was...Ch. 8.2 - 8-39. The compressive strength of concrete is...Ch. 8.2 - 8-40. A machine produces metal rods used in an...Ch. 8.2 - 8-41. An article in Computers & Electrical...Ch. 8.2 - Prob. 42ECh. 8.2 - 8-43. An article in Nuclear Engineering...Ch. 8.2 - Prob. 44ECh. 8.2 - 8-45. A healthcare provider monitors the number of...Ch. 8.3 - 8-46. Q Determine the values of the following...Ch. 8.3 - Prob. 47ECh. 8.3 - 8-48. A rivet is to be inserted into a hole. A...Ch. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - 8-54. An article in Cancer Research [“Analyses of...Ch. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.4 - 8-59. The fraction of defective integrated...Ch. 8.4 - Prob. 60ECh. 8.4 - 8-61. The 2004 presidential election exit polls...Ch. 8.4 - 8-62. Of 1000 randomly selected cases of lung...Ch. 8.4 - 8-63. An article in the Journal of the American...Ch. 8.4 - 8-64. A random sample of 50 suspension helmets...Ch. 8.4 - 8-65. The Arizona Department of Transportation...Ch. 8.4 - 8-66. A study is to be conducted of the percentage...Ch. 8.4 - 8-67. The U.S. Postal Service (USPS) has used...Ch. 8.4 - Prob. 68ECh. 8.4 - Prob. 69ECh. 8.4 - Prob. 70ECh. 8.4 - Prob. 72ECh. 8.6 - 8-73. Go Tutorial Consider the tire-testing data...Ch. 8.6 - 8-74. Consider the Izod impact test described in...Ch. 8.6 - 8-75. Consider the syrup-dispensing measurements...Ch. 8.6 - Prob. 76ECh. 8.6 - Prob. 77ECh. 8.6 - 8-78. Consider the margarine test described in...Ch. 8.6 - Prob. 79ECh. 8.6 - Prob. 80ECh. 8.6 - 8-81. Consider the test on the compressive...Ch. 8.6 - Prob. 82ECh. 8.6 - 8-83. Consider the fuel rod enrichment data...Ch. 8.6 - Prob. 84ECh. 8.6 - 8-85. Consider the tire-testing data in Exercise...Ch. 8.6 - Prob. 86ECh. 8.6 - Prob. 87ECh. 8.6 - 8-88. Consider the margarine test described in...Ch. 8.6 - Prob. 89ECh. 8.6 - Prob. 90ECh. 8.6 - 8-91. Consider the television tube brightness data...Ch. 8.6 - Prob. 92ECh. 8.6 - Prob. 93ECh. 8.6 - Prob. 94ECh. 8 - Prob. 95SECh. 8 - 8-96. A normal population has a known mean of 50...Ch. 8 - 8-97. A normal population has known mean μ = 50...Ch. 8 - 8-98. An article in the Journal of Sports Science...Ch. 8 - 8-99. The article “Mix Design for Optimal Strength...Ch. 8 - 8-100. An operating system for a personal computer...Ch. 8 - 8-101. Consider the hemoglobin data in Exercise...Ch. 8 - Prob. 102SECh. 8 - 8-103. The maker of a shampoo knows that customers...Ch. 8 - 8-104. During the 1999 and 2000 baseball seasons,...Ch. 8 - Prob. 105SECh. 8 - 8-106 An article in the ASCE Journal of Energy...Ch. 8 - 8-107. The tar content in 30 samples of cigar...Ch. 8 - Prob. 108SECh. 8 - Prob. 109SECh. 8 - Prob. 110SECh. 8 - 8-111. An article in the Journal of Applied...Ch. 8 - Prob. 112SECh. 8 - Prob. 113SECh. 8 - Prob. 114SECh. 8 - Prob. 115SECh. 8 - Prob. 116SECh. 8 - Prob. 117SECh. 8 - Prob. 118SECh. 8 - Prob. 119SE
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