Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 6, Problem 119SE
To determine
Construct a box plot of the yardage distance and interpret.
Explain whether the box plot compare in interpretive value to the original stem-and-leaf diagram.
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Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 203.8 ft and standard deviation 43.8 ft.
You intend to measure a random sample of n = 211trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis (each tick mark) is one standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places.
Image attached. I filled in the yellow boxes and am not sure why they are wrong. There are 3 yellow boxes filled in with values 206.82; 209.84; 212.86.
Could you please answer this question using excel.Thanks
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 6 Solutions
Applied Statistics and Probability for Engineers
Ch. 6.1 - 6-1. Will the sample mean always correspond to one...Ch. 6.1 - 6-2. Will exactly half of the observations in a...Ch. 6.1 - Prob. 3ECh. 6.1 - 6-4. For any set of data values, is it possible...Ch. 6.1 - 6-5. Can the sample standard deviation be equal to...Ch. 6.1 - 6-6. Suppose that you add 10 to all of the...Ch. 6.1 - 6-7. Eight measurements were made on the inside...Ch. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - 6-10. An article in the Journal of Structural...
Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - 6-14. Preventing fatigue crack propagation in...Ch. 6.1 - 6-15. An article in the Journal of Physiology...Ch. 6.1 - Prob. 16ECh. 6.1 - 6-17. The pH of a solution is measured eight times...Ch. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - 6-22. Cloud seeding, a process in which chemicals...Ch. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.2 - 6-25. For the data in Exercise 6-20,
(a) Construct...Ch. 6.2 - 6-26. For the data in Exercise 6-21,
(a) Construct...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - 6-30. An article in Technometrics (1977, Vol. 19,...Ch. 6.2 - 6-31. Go Tutorial The following data are the...Ch. 6.2 - Prob. 32ECh. 6.2 - 6-33. The following data represent the yield on 90...Ch. 6.2 - 6-34. Calculate the sample median, mode, and mean...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - 6-40. An important quality characteristic of water...Ch. 6.2 - Prob. 41ECh. 6.2 - 6-42. A semiconductor manufacturer produces...Ch. 6.2 - Prob. 43ECh. 6.2 - 6-44. In their book Introduction to Linear...Ch. 6.2 - Prob. 45ECh. 6.3 - 6-46. Construct a frequency distribution and...Ch. 6.3 - 6-47. Construct a frequency distribution and...Ch. 6.3 - 6-48. Construct a frequency distribution and...Ch. 6.3 - Prob. 49ECh. 6.3 - 6-50. Construct frequency distributions and...Ch. 6.3 - 6-51. Construct histograms with 8 and 16 bins for...Ch. 6.3 - 6-52. Construct histograms with 8 and 16 bins for...Ch. 6.3 - Prob. 53ECh. 6.3 - 6-54. Construct a histogram for the female student...Ch. 6.3 - 6-55. Construct a histogram for the spot weld...Ch. 6.3 - 6-56. Construct a histogram for the water quality...Ch. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - 6-59. Construct a histogram for the pinot noir...Ch. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - 6-63. Construct a frequency distribution and...Ch. 6.3 - Prob. 64ECh. 6.4 - 6-65. Using the data on bridge conditions from...Ch. 6.4 - 6-66. Using the data on acid rain from Exercise...Ch. 6.4 - 6-67. Using the data from Exercise 6-22 on cloud...Ch. 6.4 - 6-68. Using the data from Exercise 6-24 on swim...Ch. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - 6-71. The nine measurements that follow are...Ch. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - 6-80 In Exercise 6-69, data were presented on the...Ch. 6.4 - 6-81. An article in Nature Genetics...Ch. 6.5 - 6-82. The following data are the viscosity...Ch. 6.5 - Prob. 83ECh. 6.5 - 6-84. In their book Time Series Analysis,...Ch. 6.5 - Prob. 85ECh. 6.5 - Prob. 86ECh. 6.5 - Prob. 87ECh. 6.5 - Prob. 88ECh. 6.5 - Prob. 89ECh. 6.6 - Prob. 90ECh. 6.6 - Prob. 91ECh. 6.6 - 6-92. An article in the Journal of Pharmaceuticals...Ch. 6.7 - 6-93. Construct a normal probability plot of the...Ch. 6.7 - 6-94. Construct a normal probability plot of the...Ch. 6.7 - Prob. 95ECh. 6.7 - 6-96. Construct a normal probability plot of the...Ch. 6.7 - Prob. 97ECh. 6.7 - 6-98. Construct a normal probability plot of the...Ch. 6.7 - Prob. 99ECh. 6.7 - 6-100. Construct a normal probability plot of the...Ch. 6.7 - Prob. 101ECh. 6.7 - Prob. 102ECh. 6 - Prob. 103SECh. 6 - 6-104. The concentration of a solution is measured...Ch. 6 - 6-105. Table 6E.10 shows unemployment data for the...Ch. 6 - 6-106. A sample of six resistors yielded the...Ch. 6 - 6-107. Consider the following two samples:
Sample...Ch. 6 - 6-108. An article in Quality Engineering (1992....Ch. 6 - Prob. 109SECh. 6 - Prob. 110SECh. 6 - Prob. 111SECh. 6 - Prob. 112SECh. 6 - 6-113. Q A manufacturer of coil springs is...Ch. 6 - 6-114. A communication channel is being monitored...Ch. 6 - Prob. 115SECh. 6 - Prob. 116SECh. 6 - 6-117. Construct a normal probability plot of the...Ch. 6 - Prob. 118SECh. 6 - Prob. 119SECh. 6 - Prob. 120SECh. 6 - Prob. 121SECh. 6 - 6-122. In 1789, Henry Cavendish estimated the...Ch. 6 - Prob. 123SECh. 6 - 6-124. Patients arriving at a hospital emergency...Ch. 6 - Prob. 125SECh. 6 - 6-126. The energy consumption for 90 gas-heated...Ch. 6 - Prob. 127SECh. 6 - Prob. 128SECh. 6 - Prob. 129SECh. 6 - Prob. 130SECh. 6 - Prob. 131SECh. 6 - Prob. 132SECh. 6 - Prob. 133SECh. 6 - Prob. 134SECh. 6 - Prob. 135SECh. 6 - Prob. 136SECh. 6 - Prob. 137SE
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