An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 9.2, Problem 1Q
Some states that operate a lottery believe that restricting the use of lottery profits to supporting education makes the lottery more profitable. Other states permit general use of the lottery income. The profitability of the lottery for a group of states in each category is given below.
| State Lottery Profits | |||
| For Education | For General Use | ||
| State | % Profit | State | % Profit |
| New Mexico | 24 | Massachusetts | 21 |
| Idaho | 25 | Maine | 22 |
| Kentucky | 28 | Iowa | 24 |
| South Carolina | 28 | Colorado | 27 |
| Georgia | 28 | Indiana | 27 |
| Missouri | 29 | Dist. Columbia | 28 |
| Ohio | 29 | Connecticut | 29 |
| Tennessee | 31 | Pennsylvania | 32 |
| Florida | 31 | Maryland | 32 |
| California | 35 | ||
| North Carolina | 35 | ||
| New Jersey | 35 | ||
Data from: New York Times, National Section, October 7, 2007, p. 14.
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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 9 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
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