Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134685779
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4.2, Problem 1BSC
Notation When randomly selecting an adult, A denotes the
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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 4 Solutions
Essentials of Statistics (6th Edition)
Ch. 4.1 - New Jersey Lottery Let A denote the event of...Ch. 4.1 - Probability Rewrite the following statement so...Ch. 4.1 - Interpreting Weather While this exercise was being...Ch. 4.1 - Subjective Probability Estimate the probability...Ch. 4.1 - Identifying Probability Values Which of the...Ch. 4.1 - Penicillin Who discovered penicillin: Sean Penn,...Ch. 4.1 - Avogadro Constant If you are asked on a quiz to...Ch. 4.1 - Births Example 2 in this section includes the...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...
Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - SAT Test When making a random guess for an answer...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - Randomness When using a computer to randomly...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Kentucky Pick 4 In the Kentucky Pick 4 lottery,...Ch. 4.1 - Finding Odds in Roulette A roulette wheel has 38...Ch. 4.1 - Kentucky Derby Odds When the horse California...Ch. 4.1 - Relative Risk and Odds Ratio In a clinical trial...Ch. 4.2 - Notation When randomly selecting an adult, A...Ch. 4.2 - Notation When randomly selecting adults, let M...Ch. 4.2 - Sample for a Poll There are 15,524,971 adults in...Ch. 4.2 - Rule of Complements When randomly selecting an...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20; use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - In Exercises 29 and 30, find the probabilities and...Ch. 4.2 - Prob. 30BSCCh. 4.2 - Surge Protectors Refer to the accompanying figure...Ch. 4.2 - Prob. 32BBCh. 4.2 - Exclusive Or The exclusive or means either one or...Ch. 4.2 - Complements and the Addition Rule Refer to the...Ch. 4.3 - Language: Complement of At Least One Let A = the...Ch. 4.3 - Probability of At Least One Let A = the event of...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Probability of a Girl Assuming that boys and girls...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - Redundancy in Computer Hard Drives Assume that...Ch. 4.3 - Redundancy in Stadium Generators Large stadiums...Ch. 4.3 - Composite Drug Test Based on the data in Table 4-1...Ch. 4.3 - Composite Water Samples The Fairfield County...Ch. 4.3 - Shared Birthdays Find the probability that of 25...Ch. 4.4 - Notation What does the symbol ! represent? Six...Ch. 4.4 - New Jersey Pick 6 In the New Jersey Pick 6 lottery...Ch. 4.4 - Oregon Pick 4 In the Oregon Pick 4 lottery game, a...Ch. 4.4 - Combination Lock The typical combination lock uses...Ch. 4.4 - In Exercises 536, express all probabilities as...Ch. 4.4 - Social Security Numbers A Social Security number...Ch. 4.4 - Quinela In a horse race, a quinela bet is won if...Ch. 4.4 - Soccer Shootout In soccer, a tie at the end of...Ch. 4.4 - Grading Exams Your professor has just collected...Ch. 4.4 - Radio Station Call Letters If radio station call...Ch. 4.4 - Scheduling Routes A presidential candidate plans...Ch. 4.4 - Survey Reliability A survey with 12 questions is...Ch. 4.4 - Safety with Numbers The author owns a safe in...Ch. 4.4 - Electricity When testing for current in a cable...Ch. 4.4 - Sorting Hat At Hogwarts School of Witchcraft and...Ch. 4.4 - Moving Company The United Van Lines moving company...Ch. 4.4 - Powerball As of this writing, the Powerball...Ch. 4.4 - Teed Off When four golfers are about to begin a...Ch. 4.4 - ZIP Code If you randomly select five digits, each...Ch. 4.4 - FedEx Deliveries With a short time remaining in...Ch. 4.4 - Phone Numbers Current rules for telephone area...Ch. 4.4 - Classic Counting Problem A classic counting...Ch. 4.4 - Corporate Officers and Committees The Digital Pet...Ch. 4.4 - ATM You want to obtain cash by using an ATM, but...Ch. 4.4 - Party Mix DJ Marty T is hosting a party tonight...Ch. 4.4 - Identity Theft with Credit Cards Credit card...Ch. 4.4 - What a Word! One of the longest words in standard...Ch. 4.4 - Phase I of a Clinical Trial A clinical test on...Ch. 4.4 - Mega Millions As of this writing, the Mega...Ch. 4.4 - Designing Experiment Clinical trials of Nasonex...Ch. 4.4 - Morse Codes The International Morse code is a way...Ch. 4.4 - Mendels Peas Mendel conducted some his famous...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Counting with Fingers How many different ways can...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Win 1 Billion Quicken Loans offered a prize of 1...Ch. 4.4 - Computer Variable Names A common computer...Ch. 4.4 - High Fives a. Five mathletes celebrate after...Ch. 4 - Standard Tests Standard tests, such as the SAT or...Ch. 4 - Rain As the author is creating this exercise, a...Ch. 4 - Months If a month is randomly selected after...Ch. 4 - Social Networking Based on data from the Pew...Ch. 4 - Subjective Probability Estimate the probability...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 10RECh. 4 - Black Cars Use subjective probability to estimate...Ch. 4 - Vision Correction About 75% of the U.S. population...Ch. 4 - National Statistics Day a. If a person is randomly...Ch. 4 - Composite Sampling for Diabetes Currently, the...Ch. 4 - Wild Card Lottery The Wild Card lottery is run in...Ch. 4 - Pennsylvania Cash 5 In the Pennsylvania Cash 5...Ch. 4 - Redundancy Using Braun battery-powered alarm...Ch. 4 - Exacta In a horse race, an exacta bet is won by...Ch. 4 - Fatal Drunk Driving Listed below are the blood...Ch. 4 - Fatal Drunk Driving Use the same data given in...Ch. 4 - Organ Donors USA Today provided information about...Ch. 4 - Sampling Eye Color Based on a study by Dr. P....Ch. 4 - Prob. 5CRECh. 4 - New Lottery Game In the Monopoly Millionaires Club...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...
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