Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 7, Problem 19RE
List the properties of the normal density curve.
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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.
To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012).
Brand & Model
Price ($)
Overall Score
Samsung Ultrabook NP900X3C-A01US
1250
83
Apple MacBook Air MC965LL/A
1300
83
Apple MacBook Air MD231LL/A
1200
82
HP ENVY 13-2050nr Spectre XT
950
79
Sony VAIO SVS13112FXB
800
77
Acer Aspire S5-391-9880 Ultrabook
1200
74
Apple MacBook Pro MD101LL/A
1200
74
Apple MacBook Pro MD313LL/A
1000
73
Dell Inspiron I13Z-6591SLV
700
67
Samsung NP535U3C-A01US
600
63
a. Select a scatter diagram with price as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship…
To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow.
Adjusted Gross Income ($1000s)
Reasonable Amount ofItemized Deductions ($1000s)
22
9.6
27
9.6
32
10.1
48
11.1
65
13.5
85
17.7
120
25.5
Compute b1 and b0 (to 4 decimals).b1 b0 Complete the estimated regression equation (to 2 decimals). = + x
Predict a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52.5 thousand (to 2 decimals). thousand dollarsWhat is the value, in dollars, of…
Chapter 7 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 7.1 - A _____ _____ _____ is an equation used to compute...Ch. 7.1 - A _______ is an equation, table, or graph used to...Ch. 7.1 - True or False: The normal curve is symmetric about...Ch. 7.1 - The area under the normal curve to the right of ...Ch. 7.1 - The points at x = _____ and x = _____ are the...Ch. 7.1 - The area under a normal curve can be interpreted...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - Prob. 10AYU
Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - For Problems 712, determine whether the graph can...Ch. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Prob. 15AYUCh. 7.1 - Problems 1316 use the information presented in...Ch. 7.1 - Uniform Distribution The random-number generator...Ch. 7.1 - Uniform Distribution The reaction time X (in...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - In Problems 1922, determine whether or not the...Ch. 7.1 - One graph in the figure on the following page...Ch. 7.1 - One graph in the figure below represents a normal...Ch. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - Prob. 27AYUCh. 7.1 - In Problems 2528, the graph of a normal curve is...Ch. 7.1 - In Problems 29 and 30, draw a normal curve and...Ch. 7.1 - Prob. 30AYUCh. 7.1 - NW You Explain It! Cell Phone Rates Monthly...Ch. 7.1 - You Explain It! Refrigerators The lives of...Ch. 7.1 - You Explain It! Birth Weights The birth weights of...Ch. 7.1 - You Explain It! Height of 10-Year-Old Males The...Ch. 7.1 - NW You Explain It! Gestation Period The lengths of...Ch. 7.1 - Prob. 36AYUCh. 7.1 - Hitting with a Pitching Wedge In the game of golf,...Ch. 7.1 - Heights of Five-Year-Old Females The following...Ch. 7.1 - Cardiac Arrest Researchers conducted a prospective...Ch. 7.2 - A random variable Z that is normally distributed...Ch. 7.2 - The notation z is the z-score such that the area...Ch. 7.2 - If X is a normal random variable with mean 40 and...Ch. 7.2 - If X is normal random variable with mean 40 and...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 512, find the indicated areas. For...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1318, find the indicated z-score. Be...Ch. 7.2 - In Problems 1922, find the value of z. 19. NW...Ch. 7.2 - In Problems 1922, find the value of z. 20. z0.02Ch. 7.2 - In Problems 1922, find the value of z. 21. z0.025Ch. 7.2 - In Problems 1922, find the value of z. 22. z0.015Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 2332, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - In Problems 3336, assume that the random variable...Ch. 7.2 - Egg Incubation Times The mean incubation time of...Ch. 7.2 - Reading Rates The reading speed of sixth-grade...Ch. 7.2 - NW Chips Ahoy! Cookies The number of chocolate...Ch. 7.2 - Wendys Drive-Through Fast-food restaurants spend...Ch. 7.2 - Gestation Period The lengths of human pregnancies...Ch. 7.2 - Light Bulbs General Electric manufactures a...Ch. 7.2 - Manufacturing Steel rods are manufactured with a...Ch. 7.2 - Manufacturing Ball bearings are manufactured with...Ch. 7.2 - NCAA Basketball Point Spreads In sports betting,...Ch. 7.2 - Prob. 46AYUCh. 7.2 - NW Egg Incubation Times The mean incubation time...Ch. 7.2 - Reading Rates The reading speed of sixth-grade...Ch. 7.2 - Chips Ahoy! Cookies The number of chocolate chips...Ch. 7.2 - Wendys Drive-Through Fast-food restaurants spend...Ch. 7.2 - Speedy Lube The time required for Speedy Lube to...Ch. 7.2 - Putting It Together: Birth Weights The following...Ch. 7.2 - Prob. 53AYUCh. 7.2 - Prob. 54AYUCh. 7.2 - Explain why P(X 220) should be reported as ...Ch. 7.2 - The ACT and SAT are two college entrance exams....Ch. 7.3 - A _____ _____ _____ is a graph that plots observed...Ch. 7.3 - True or False: A normal score is the expected...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 36, use the results in the table to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - In Problems 710, use a normal probability plot to...Ch. 7.3 - Chips per Bag In a 1998 advertising campaign,...Ch. 7.3 - Hours of TV A random sample of college students...Ch. 7.3 - Putting It Together: Demon Roller Coaster Retrieve...Ch. 7.4 - In a binomial experiment with n trials and...Ch. 7.4 - When adding or subtracting 0.5 from X, we are...Ch. 7.4 - Suppose X is a binomial random variable. To...Ch. 7.4 - Suppose X is a binomial random variable. To...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 9AYUCh. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 11AYUCh. 7.4 - In Problems 514, a discrete random variable is...Ch. 7.4 - Prob. 13AYUCh. 7.4 - Prob. 14AYUCh. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - In Problems 1520, compute P(x) using the binomial...Ch. 7.4 - Prob. 19AYUCh. 7.4 - Prob. 20AYUCh. 7.4 - NW On-Time Flights According to American Airlines,...Ch. 7.4 - Prob. 22AYUCh. 7.4 - Prob. 23AYUCh. 7.4 - Sneeze According to a study done by Nick Wilson of...Ch. 7.4 - Males Living at Home According to the Current...Ch. 7.4 - Females Living at Home According to the Current...Ch. 7.4 - NW Boys Are Preferred In a Gallup poll, 37% of...Ch. 7.4 - Liars According to a USA Today Snapshot, 3% of...Ch. 7 - Use the figure to answer the questions that...Ch. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - In Problems 2 and 3, draw a standard normal curve...Ch. 7 - Find the z-score such that the area to the right...Ch. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Tire Wear Suppose that Dunlop Tire manufactures a...Ch. 7 - Wechsler Intelligence Scale The Wechsler...Ch. 7 - Major League Baseballs According to Major League...Ch. 7 - America Reads According to a Gallup poll, 46% of...Ch. 7 - Prob. 14RECh. 7 - Hector obtained a random sample of twenty recent...Ch. 7 - Density of Earth In 1798, Henry Cavendish obtained...Ch. 7 - Creative Thinking According to a USA Today...Ch. 7 - A continuous random variable X is uniformly...Ch. 7 - List the properties of the normal density curve.Ch. 7 - Prob. 20RECh. 7 - Prob. 1CTCh. 7 - Prob. 2CTCh. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Suppose that the talk time on the Apple iPhone is...Ch. 7 - The waist circumference of males 2029 years old is...Ch. 7 - Suppose the scores earned on Professor McArthurs...Ch. 7 - In a poll conducted by the Gallup organization,...Ch. 7 - Prob. 10CTCh. 7 - A continuous random variable X is uniformly...Ch. 7 - The reference interval for HDL cholesterol is...
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