
Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 3, Problem 205SE
a.
To determine
Find the
b.
To determine
Find the probability mass function of the number of customers that replay if the company samples 10 customers.
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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.
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate
it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have
on r?
Row 1
Row 2
13
149
25
36
41
60
62
78
S
205
122
195
173
133
197
24
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values.
r=0.164 (Round to three decimal places as needed.)
S
24
Chapter 3 Solutions
Applied Statistics and Probability for Engineers
Ch. 3.1 - Prob. 1ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - Prob. 7ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...
Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.2 - 3-16. The sample space of a random experiment is...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - 3-22. Consider the hospital patients in Example...Ch. 3.2 - 3-23. An article in Knee Surgery, Sports...Ch. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - 3-26. The space shuttle flight control system...Ch. 3.2 - 3-27. A disk drive manufacturer sells storage...Ch. 3.2 - 3-28. Marketing estimates that a new instrument...Ch. 3.2 - 3-29. The distributor of a machine for cytogenics...Ch. 3.2 - 3-30. An assembly consists of two mechanical...Ch. 3.2 - 3-31. An assembly consists of three mechanical...Ch. 3.2 - 3-32. The data from 200 endothermic reactions...Ch. 3.2 - 3-33. Actual lengths of stay at a hospital’s...Ch. 3.2 - 3-34. The distribution of the time until a Web...Ch. 3.2 - 3-35 The following table shows the typical depth...Ch. 3.2 - 3-36. Consider the wafers with contamination...Ch. 3.2 - 3-37. Consider the circuit in Example 2-32. Assume...Ch. 3.3 - 3-38. Determine the cumulative distribution...Ch. 3.3 - 3-39. Determine the cumulative distribution...Ch. 3.3 - 3-40. Determine the cumulative distribution...Ch. 3.3 - 3-41. Determine the cumulative distribution...Ch. 3.3 - 3-42. Determine the cumulative distribution...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - 3-45. Determine the cumulative distribution...Ch. 3.3 - Prob. 46ECh. 3.3 - 3-47. Determine the cumulative distribution...Ch. 3.3 - 3-48. Determine the cumulative distribution...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - 3-53. Determine the cumulative distribution...Ch. 3.3 - 3-54. Determine the cumulative distribution...Ch. 3.3 - 3-55. Determine the cumulative distribution...Ch. 3.3 - 3-56. Determine the cumulative distribution...Ch. 3.4 - 3-57. If the range of X is the set {0,1,2,3,4} and...Ch. 3.4 - 3-58. Determine the mean and variance of the...Ch. 3.4 - 3-59. Determine the mean and variance of the...Ch. 3.4 - 3-60. Determine the mean and variance of the...Ch. 3.4 - 3-61. Determine the mean and variance of the...Ch. 3.4 - Prob. 62ECh. 3.4 - 3-63. Determine the mean and variance of the...Ch. 3.4 - Prob. 64ECh. 3.4 - 3-65. The range of the random variable X is [0, 1,...Ch. 3.4 - 3-66. In a NiCd battery, a fully charged cell is...Ch. 3.4 - 3-67. The space shuttle flight control system...Ch. 3.4 - 3-68. Trees are subjected to different levels of...Ch. 3.4 - 3-69. An article in the Journal of Database...Ch. 3.4 - 3-70. Calculate the mean and variance for the...Ch. 3.4 - 3-71. Calculate the mean and variance for the...Ch. 3.4 - 3-72. Calculate the mean and variance for the...Ch. 3.4 - 3-73. Calculate the mean and variance for the...Ch. 3.4 - 3-74. Calculate the mean and variance for the...Ch. 3.4 - 3-75. Calculate the mean for the random variable...Ch. 3.5 - 3-76. Let the random variable X have a discrete...Ch. 3.5 - 3-77. Let the random variable X have a discrete...Ch. 3.5 - 3-78. Thickness measurements of a coating process...Ch. 3.5 - Prob. 79ECh. 3.5 - 3-80. The lengths of plate glass parts are...Ch. 3.5 - 3-81. Assume that the wavelengths of...Ch. 3.5 - 3-82. The probability of an operator entering...Ch. 3.5 - 3-83. Suppose that X has a discrete uniform...Ch. 3.5 - 3-84. Show that for a discrete uniform random...Ch. 3.5 - 3-85. The number of pages in a PDF document you...Ch. 3.5 - 3-86. Suppose that nine-digit Social Security...Ch. 3.5 - 3-87. Suppose that 1000 seven-digit telephone...Ch. 3.5 - 3-88. The probability that data are entered...Ch. 3.5 - 3-89. Each multiple-choice question on an exam has...Ch. 3.5 - 3-90. Consider the hospital data in Example 2-8....Ch. 3.6 - 3-91. For each scenario (a)–(j), state whether or...Ch. 3.6 - 3-92. Let X be a binomial random variable with p =...Ch. 3.6 - 3-93. Let X be a binomial random variable with p =...Ch. 3.6 - 3-94. The random variable X has a binomial...Ch. 3.6 - 3-95. The random variable X has a binomial...Ch. 3.6 - 3-96. The random variable X has a binomial...Ch. 3.6 - 3-97. Sketch the probability mass function of a...Ch. 3.6 - 3-98. Determine the cumulative distribution...Ch. 3.6 - Prob. 99ECh. 3.6 - Prob. 100ECh. 3.6 - 3-101. The phone lines to an airline reservation...Ch. 3.6 - 3-102. A multiple-choice test contains 25...Ch. 3.6 - 3-103. A particularly long traffic light on your...Ch. 3.6 - 3-104. Samples of rejuvenated mitochondria are...Ch. 3.6 - Prob. 105ECh. 3.6 - 3-106. Heart failure is due to either natural...Ch. 3.6 - 3-107. A computer system uses passwords that are...Ch. 3.6 - 3-108. Samples of 20 parts from a metal punching...Ch. 3.6 - 3-109. Because all airline passengers do not show...Ch. 3.6 - 3-110. This exercise illustrates that poor quality...Ch. 3.6 - 3-111. Consider the lengths of stay at a...Ch. 3.6 - 3-112. Consider the patient data in Example 2-8....Ch. 3.6 - 3-113. Assume that a Web site changes its content...Ch. 3.6 - 3-114. Consider the endothermic reactions in...Ch. 3.6 - 3-115. The probability that a visitor to a Web...Ch. 3.6 - 3-116. Consider the circuit in Example 2-34....Ch. 3.6 - 3-117. Consider the time to recharge the flash in...Ch. 3.6 - 3-118. Consider the patient data in Example 2-8....Ch. 3.7 - 3-119. Suppose that the random variable X has a...Ch. 3.7 - Prob. 120ECh. 3.7 - 3-121. Consider a sequence of independent...Ch. 3.7 - Prob. 122ECh. 3.7 - 3-123. The probability of a successful optical...Ch. 3.7 - 3-124. In a clinical study, volunteers are tested...Ch. 3.7 - 3-125. Assume that each of your calls to a popular...Ch. 3.7 - 3-126. A player of a video game is confronted with...Ch. 3.7 - 3-127. Heart failure is due to either natural...Ch. 3.7 - 3-128. A computer system uses passwords...Ch. 3.7 - 3-129. A trading company uses eight computers to...Ch. 3.7 - 3-130. Assume that 20 parts are checked each hour...Ch. 3.7 - 3-131. A fault-tolerant system that processes...Ch. 3.7 - Prob. 132ECh. 3.7 - Prob. 133ECh. 3.7 - 3-134. Consider the endothermic reactions in...Ch. 3.7 - 3-135. A Web site randomly selects among 10...Ch. 3.7 - Prob. 136ECh. 3.7 - 3-137. Consider the time to recharge the flash in...Ch. 3.7 - 3-138. An array of 30 LED bulbs is used in an...Ch. 3.7 - Prob. 139ECh. 3.7 - 3-140. Customers visit a Web site, and the...Ch. 3.8 - 3-141. Suppose that X has a hypergeometric...Ch. 3.8 - Prob. 142ECh. 3.8 - Prob. 143ECh. 3.8 - Prob. 144ECh. 3.8 - 3-145. A research study uses 800 men under the age...Ch. 3.8 - Prob. 146ECh. 3.8 - Prob. 147ECh. 3.8 - 3-148. A state runs a lottery in which six numbers...Ch. 3.8 - Prob. 149ECh. 3.8 - 3-150. Calculate the finite population...Ch. 3.8 - 3-151. Consider the visits that result in leave...Ch. 3.8 - 3-152. Consider the nonfailed wells in Exercises...Ch. 3.8 - 3-153. Consider the semiconductor wafer data in...Ch. 3.8 - 3-154. Suppose that a healthcare provider selects...Ch. 3.8 - Prob. 155ECh. 3.8 - 3-156. A utility company might offer electrical...Ch. 3.9 - 3-157. Suppose that X has a Poisson distribution...Ch. 3.9 - Prob. 158ECh. 3.9 - Prob. 159ECh. 3.9 - 3-160. The number of telephone calls that arrive...Ch. 3.9 - 3-161. Astronomers treat the number of stars in a...Ch. 3.9 - 3-162. Data from www.centralhudsonlabs.com...Ch. 3.9 - Prob. 163ECh. 3.9 - 3-164. The number of flaws in bolts of cloth in...Ch. 3.9 - Prob. 165ECh. 3.9 - 3-166. The number of cracks in a section of...Ch. 3.9 - Prob. 167ECh. 3.9 - 3-168. The number of failures of a testing...Ch. 3.9 - 3-169. The number of content changes to a Web site...Ch. 3.9 - 3-170. The number of views of a page on a Web site...Ch. 3.9 - Prob. 171ECh. 3.9 - 3-172. Orders arrive at a Web site according to a...Ch. 3.9 - 3-173. The article “An Association Between Fine...Ch. 3.9 - 3-174. Inclusions are defects in poured metal...Ch. 3 - Prob. 175SECh. 3 - 3-176. Let X denote the number of bits received in...Ch. 3 - 3-177. Batches that consist of 50 coil springs...Ch. 3 - Prob. 178SECh. 3 - 3-179. A total of 12 cells are replicated. Freshly...Ch. 3 - Prob. 180SECh. 3 - 3-181. A particularly long traffic light on your...Ch. 3 - 3-182. The probability is 0.6 that a calibration...Ch. 3 - Prob. 183SECh. 3 - 3-184. The probability that an eagle kills a...Ch. 3 - 3-185. Traffic flow is traditionally modeled as a...Ch. 3 - 3-186. A shipment of chemicals arrives in 15...Ch. 3 - Prob. 187SECh. 3 - 3-188. The probability that your call to a service...Ch. 3 - 3-189. The probability that your call to a service...Ch. 3 - 3-190. The number of messages that arrive at a Web...Ch. 3 - Prob. 191SECh. 3 - 3-192. The number of errors in a textbook follows...Ch. 3 - Prob. 193SECh. 3 - Prob. 194SECh. 3 - 3-195. In a manufacturing process that laminates...Ch. 3 - Prob. 196SECh. 3 - Prob. 197SECh. 3 - 3-198. A manufacturer of a consumer electronics...Ch. 3 - Prob. 199SECh. 3 - 3-200. The random variable X has the following...Ch. 3 - Prob. 201SECh. 3 - Prob. 202SECh. 3 - Prob. 203SECh. 3 - 3-204. An installation technician for a...Ch. 3 - Prob. 205SECh. 3 - Prob. 206SECh. 3 - 3-207. Messages arrive to a computer server...Ch. 3 - 3-208. Flaws occur in the interior of plastic used...Ch. 3 - Prob. 209SECh. 3 - Prob. 210SECh. 3 - Prob. 211SECh. 3 - Prob. 212SECh. 3 - Prob. 213SECh. 3 - Prob. 214SECh. 3 - Prob. 215SECh. 3 - Prob. 216SECh. 3 - Prob. 217SECh. 3 - Prob. 218SECh. 3 - Prob. 219SE
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