Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 2.4, Problem 1TY
a.
To determine
To identify: The minimum and maximum salaries.
b.
To determine
To find: The
c.
To determine
To compare: The result with corporation A.
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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 2 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 2.1 - Prob. 1TYCh. 2.1 - Prob. 2TYCh. 2.1 - Prob. 3TYCh. 2.1 - Prob. 4TYCh. 2.1 - Prob. 5TYCh. 2.1 - Prob. 6TYCh. 2.1 - Prob. 7TYCh. 2.1 - What are some benefits of representing data sets...Ch. 2.1 - Why should the number of classes in a frequency...Ch. 2.1 - What is the difference between class limits and...
Ch. 2.1 - What is the difference between relative frequency...Ch. 2.1 - After constructing an expanded frequency...Ch. 2.1 - What is the difference between a frequency polygon...Ch. 2.1 - True or False? In Exercises 710, determine whether...Ch. 2.1 - True or False? In Exercises 710, determine whether...Ch. 2.1 - True or False? In Exercises 710, determine whether...Ch. 2.1 - Prob. 10ECh. 2.1 - In Exercises 1114, use the minimum and maximum...Ch. 2.1 - In Exercises 1114, use the minimum and maximum...Ch. 2.1 - In Exercises 1114, use the minimum and maximum...Ch. 2.1 - In Exercises 1114, use the minimum and maximum...Ch. 2.1 - Reading a Frequency Distribution In Exercises 15...Ch. 2.1 - Prob. 15ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Constructing a Frequency Distribution and a...Ch. 2.1 - Constructing a Frequency Distribution and a...Ch. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - In Exercises 43 and 44, use the data set and the...Ch. 2.1 - Prob. 44ECh. 2.1 - What Would You Do? You work at a bank and are...Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.2 - Prob. 1TYCh. 2.2 - Prob. 2TYCh. 2.2 - Prob. 3TYCh. 2.2 - Prob. 4TYCh. 2.2 - Prob. 5TYCh. 2.2 - Prob. 6TYCh. 2.2 - Prob. 7TYCh. 2.2 - Name some ways to display quantitative data...Ch. 2.2 - What is an advantage of using a stem-and-leaf plot...Ch. 2.2 - In terms of displaying data, how is a...Ch. 2.2 - How is a Pareto chart different from a standard...Ch. 2.2 - Putting Graphs in Context In Exercises 58, match...Ch. 2.2 - Putting Graphs in Context In Exercises 58, match...Ch. 2.2 - Putting Graphs in Context In Exercises 58, match...Ch. 2.2 - Putting Graphs in Context In Exercises 58, match...Ch. 2.2 - Graphical Analysis In Exercises 912, use the...Ch. 2.2 - Graphical Analysis In Exercises 912, use the...Ch. 2.2 - Graphical Analysis In Exercises 912, use the...Ch. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Graphing Data Sets In Exercises 1732, organize the...Ch. 2.2 - Graphing Data Sets In Exercises 1732, organize the...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Graphing Data Sets In Exercises 1732, organize the...Ch. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Hourly Wages Use a scatter plot to display the...Ch. 2.2 - Salaries Use a scatter plot to display the data...Ch. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Favorite Day of the Week Display the data below in...Ch. 2.2 - A Misleading Graph? A misleading graph is not...Ch. 2.2 - Prob. 38ECh. 2.2 - A Misleading Graph? A misleading graph is not...Ch. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.3 - Find the mean of the points scored by the 51...Ch. 2.3 - Find the median of the points scored by the 51...Ch. 2.3 - The points scored by the winning teams in the...Ch. 2.3 - Find the mode of the points scored by the 51...Ch. 2.3 - In a survey, 1534 adults were asked, How much do...Ch. 2.3 - Remove the data entry 65 from the data set in...Ch. 2.3 - In Example 7, your grade in the two-credit course...Ch. 2.3 - Use a frequency distribution to estimate the mean...Ch. 2.3 - True or False? In Exercises 14, determine whether...Ch. 2.3 - True or False? In Exercises 14, determine whether...Ch. 2.3 - True or False? In Exercises 14, determine whether...Ch. 2.3 - True or False? In Exercises 14, determine whether...Ch. 2.3 - Constructing Data Sets In Exercises 58, construct...Ch. 2.3 - Constructing Data Sets In Exercises 58, construct...Ch. 2.3 - Mean is not representative of a typical number in...Ch. 2.3 - Prob. 8ECh. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Prob. 14ECh. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Graphical Analysis In Exercises 912, determine...Ch. 2.3 - Prob. 17ECh. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Prob. 31ECh. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Finding and Discussing the Mean, Median, and Mode...Ch. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - In Exercises 3740, without performing any...Ch. 2.3 - In Exercises 3740, without performing any...Ch. 2.3 - In Exercises 3740, without performing any...Ch. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Finding a Weighted Mean In Exercises 4146, find...Ch. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Identifying the Shape of a Distribution In...Ch. 2.3 - Identifying the Shape of a Distribution In...Ch. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.3 - Data Analysis Students in an experimental...Ch. 2.3 - Trimmed Mean To find the 10% trimmed mean of a...Ch. 2.3 - Specify the lower limit to be 1 and the upper...Ch. 2.3 - Specify the lower limit to be 0 and the upper...Ch. 2.4 - Prob. 1TYCh. 2.4 - Prob. 2TYCh. 2.4 - Prob. 3TYCh. 2.4 - Prob. 4TYCh. 2.4 - Prob. 5TYCh. 2.4 - Prob. 6TYCh. 2.4 - Prob. 7TYCh. 2.4 - Prob. 8TYCh. 2.4 - Prob. 9TYCh. 2.4 - Prob. 10TYCh. 2.4 - Explain how to find the range of a data set. What...Ch. 2.4 - Explain how to find the deviation of an entry in a...Ch. 2.4 - Why is the standard deviation used more frequently...Ch. 2.4 - Explain the relationship between variance and...Ch. 2.4 - Describe the difference between the calculation of...Ch. 2.4 - Given a data set. how do you know whether to...Ch. 2.4 - Discuss the similarities and the differences...Ch. 2.4 - What must you know about a data set before you can...Ch. 2.4 - Prob. 9ECh. 2.4 - Finding the Range of a Data Set In Exercises 9 and...Ch. 2.4 - Archaeology The depths (in inches) at which 10...Ch. 2.4 - In Exercise 11, compare your answer to part (a)...Ch. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Estimating Standard Deviation Both data sets shown...Ch. 2.4 - Estimating Standard Deviation Both data sets shown...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Constructing Data Sets In Exercises 2528,...Ch. 2.4 - Constructing Data Sets In Exercises 2528,...Ch. 2.4 - Constructing Data Sets In Exercises 2528,...Ch. 2.4 - Constructing Data Sets In Exercises 2528,...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using the Empirical Rule In Exercises 2934, use...Ch. 2.4 - Using Chebychevs Theorem You are conducting a...Ch. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Estimating the Sample Mean and Standard Deviation...Ch. 2.4 - Estimating the Sample Mean and Standard Deviation...Ch. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Specify the lower limit to be 10 and the upper...Ch. 2.4 - Specify the lower limit to be 30 and the upper...Ch. 2.4 - Prob. 1CSCh. 2.4 - Prob. 2CSCh. 2.4 - Prob. 3CSCh. 2.4 - Prob. 4CSCh. 2.4 - Prob. 5CSCh. 2.4 - Prob. 6CSCh. 2.5 - Prob. 1TYCh. 2.5 - Prob. 2TYCh. 2.5 - Prob. 3TYCh. 2.5 - Prob. 4TYCh. 2.5 - Prob. 5TYCh. 2.5 - Prob. 6TYCh. 2.5 - Prob. 7TYCh. 2.5 - Prob. 8TYCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Explain how to identify outliers using the...Ch. 2.5 - Describe the relationship between quartiles and...Ch. 2.5 - True or False? In Exercises 710, determine whether...Ch. 2.5 - True or False? In Exercises 710, determine whether...Ch. 2.5 - True or False? In Exercises 710, determine whether...Ch. 2.5 - True or False? In Exercises 710, determine whether...Ch. 2.5 - Finding Quartiles, Interquartile Range, and...Ch. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Drawing a Box-and-Whisker Plot In Exercises 1518,...Ch. 2.5 - Drawing a Box-and-Whisker Plot In Exercises 1518,...Ch. 2.5 - Drawing a Box-and-Whisker Plot In Exercises 1518,...Ch. 2.5 - Prob. 20ECh. 2.5 - Graphical Analysis In Exercises 1922, use the...Ch. 2.5 - Graphical Analysis In Exercises 1922, use the...Ch. 2.5 - Graphical Analysis In Exercises 1922, use the...Ch. 2.5 - Graphical Analysis In Exercises 1922, use the...Ch. 2.5 - Prob. 25ECh. 2.5 - Using Technology to Find Quartiles and Draw Graphs...Ch. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Finding a Percentile In Exercises 3336, use the...Ch. 2.5 - Finding a Percentile In Exercises 3336, use the...Ch. 2.5 - Finding a Percentile In Exercises 3336, use the...Ch. 2.5 - Finding a Percentile In Exercises 3336, use the...Ch. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Life Spans of Tires A brand of automobile tire has...Ch. 2.5 - Life Spans of Fruit Flies The life spans of a...Ch. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Song Lengths Side-by-side box-and-whisker plots...Ch. 2.5 - Credit Card Purchases The credit card purchases...Ch. 2.5 - Modified Box-and-Whisker Plot In Exercises 5962,...Ch. 2.5 - Modified Box-and-Whisker Plot In Exercises 5962,...Ch. 2 - Prob. 2.1.1RECh. 2 - Prob. 2.1.2RECh. 2 - Prob. 2.1.3RECh. 2 - Prob. 2.1.4RECh. 2 - Prob. 2.1.5RECh. 2 - Prob. 2.1.6RECh. 2 - Prob. 2.2.7RECh. 2 - Prob. 2.2.8RECh. 2 - Prob. 2.2.9RECh. 2 - Prob. 2.2.10RECh. 2 - Prob. 2.2.11RECh. 2 - Prob. 2.2.12RECh. 2 - Prob. 2.3.13RECh. 2 - Prob. 2.3.14RECh. 2 - For the six test scores 78, 72, 86, 91, 87, and...Ch. 2 - For the four test scores 96, 85, 91, and 86, the...Ch. 2 - Estimate the mean of the frequency distribution...Ch. 2 - The frequency distribution shows the numbers of...Ch. 2 - Prob. 2.3.19RECh. 2 - Prob. 2.3.20RECh. 2 - In Exercises 21 and 22, determine whether the...Ch. 2 - In Exercises 21 and 22, determine whether the...Ch. 2 - Prob. 2.3.23RECh. 2 - For the histogram in Exercise 21, which is...Ch. 2 - In Exercises 25 and 26, find the range, mean,...Ch. 2 - Prob. 2.4.26RECh. 2 - Prob. 2.4.27RECh. 2 - Prob. 2.4.28RECh. 2 - Prob. 2.4.29RECh. 2 - Prob. 2.4.30RECh. 2 - Prob. 2.4.31RECh. 2 - Prob. 2.4.32RECh. 2 - From a random sample of households, the numbers of...Ch. 2 - From a random sample of airplanes, the numbers of...Ch. 2 - In Exercises 35 and 36, find the coefficient of...Ch. 2 - Prob. 2.4.36RECh. 2 - Prob. 2.5.37RECh. 2 - Prob. 2.5.38RECh. 2 - Prob. 2.5.39RECh. 2 - Prob. 2.5.40RECh. 2 - Prob. 2.5.41RECh. 2 - Prob. 2.5.42RECh. 2 - A students test grade of 75 represents the 65th...Ch. 2 - Prob. 2.5.44RECh. 2 - Prob. 2.5.45RECh. 2 - Prob. 2.5.46RECh. 2 - Prob. 2.5.47RECh. 2 - Prob. 2.5.48RECh. 2 - Prob. 1CQCh. 2 - Prob. 2CQCh. 2 - Prob. 3CQCh. 2 - Prob. 4CQCh. 2 - Prob. 5CQCh. 2 - Prob. 6CQCh. 2 - Prob. 7CQCh. 2 - Prob. 1CTCh. 2 - Prob. 2CTCh. 2 - Prob. 3CTCh. 2 - Prob. 4CTCh. 2 - Prob. 5CTCh. 2 - Prob. 6CTCh. 2 - Prob. 7CTCh. 2 - Prob. 8CTCh. 2 - Prob. 1RSRDCh. 2 - Prob. 2RSRDCh. 2 - Prob. 3RSRDCh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 5TCh. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - In Exercices 1 and 2, identify the sampling...Ch. 2 - Prob. 2CRCh. 2 - Prob. 3CRCh. 2 - Prob. 4CRCh. 2 - Prob. 5CRCh. 2 - Prob. 6CRCh. 2 - Prob. 7CRCh. 2 - Prob. 8CRCh. 2 - Prob. 9CRCh. 2 - Prob. 10CRCh. 2 - Prob. 11CRCh. 2 - Prob. 12CRCh. 2 - Prob. 13CRCh. 2 - Prob. 14CRCh. 2 - Tail lengths (in feet) for a sample of American...Ch. 2 - Prob. 16CRCh. 2 - Prob. 17CRCh. 2 - Prob. 18CRCh. 2 - Prob. 19CR
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