Understanding Basic Statistics
8th Edition
ISBN: 9781337558075
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Textbook Question
Chapter 7, Problem 1LCWP
If you look up the word empirical in a dictionary, you will find that it
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11. Suppose that the events (An, n ≥ 1) are independent. Show that the inclusion-
exclusion formula reduces to
P(UAL)-1-(1-P(Ak)).
k=1
k=1
8. Show that, if {Xn, n≥ 1} are independent random variables, then
sup X,, A) < ∞ for some A.
20. Define the o-field R2. Explain its relation to the o-field R.
Chapter 7 Solutions
Understanding Basic Statistics
Ch. 7.1 - Statistical Literacy Which, if any, of the curves...Ch. 7.1 - Statistical Literacy Look at the normal curve in...Ch. 7.1 - Critical Thinking Look at the two normal curves in...Ch. 7.1 - Critical Thinking Sketch a normal curve (a) with...Ch. 7.1 - Basic Computation: Empirical Rule What percentage...Ch. 7.1 - Basic Computation: Empirical Rule What percentage...Ch. 7.1 - Distribution: Heights of Coeds Assuming that the...Ch. 7.1 - Distribution: Rhode Island Red Chicks The...Ch. 7.1 - Archaeology: Tree Rings At Burnt Mesa Pueblo,...Ch. 7.1 - Vending Machine: Soft Drinks A vending machine...
Ch. 7.1 - Pain Management: Laser Therapy Effect of...Ch. 7.1 - Expand Your knowledge: Continuous Uniform...Ch. 7.1 - Unifrom Distribution: Measurement Errors...Ch. 7.2 - Statistical Literacy What does a standard score...Ch. 7.2 - Statistical Literacy Does a raw score less than...Ch. 7.2 - Statistical Literacy What is the value of the...Ch. 7.2 - Statistical Literacy What are the values of the...Ch. 7.2 - Basic Computation: z Score and Raw Score A normal...Ch. 7.2 - Basic Computation: z Score and Raw Score A normal...Ch. 7.2 - Critical Thinking Consider the following scores:...Ch. 7.2 - Critical Thinking Raul received a score of 80 on a...Ch. 7.2 - z Scores: First Aid Course The college physical...Ch. 7.2 - z Scores: Fawns Fawns between 1 and 5 months old...Ch. 7.2 - z Scores: Red Blood Cell Count Let x = red blood...Ch. 7.2 - Normal Curve: Tree Rings Tree-ring dates were used...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Prob. 22PCh. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Areas Under the...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.2 - Basic Computation: Finding Probabilities In...Ch. 7.3 - Statistical Literacy Consider a normal...Ch. 7.3 - Statistical Literacy Suppose 5% of the area under...Ch. 7.3 - Statistical Literacy Suppose 5% of the area under...Ch. 7.3 - Critical Thinking: Normality Consider the...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find Probabilities In Problems...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Basic Computation: Find zValues In Problems 15-24,...Ch. 7.3 - Medical: Blood Glucose A person's blood glucose...Ch. 7.3 - Medical: Blood Protoplasm Porphyrin is a pigment...Ch. 7.3 - 27 Archaeology: Hopi Village Thickness...Ch. 7.3 - Law Enforcement: Police Response Time Police...Ch. 7.3 - Guarantee: Batteries Quick Start Company makes...Ch. 7.3 - Guarantee: Watches Accrotime is a manufacturer of...Ch. 7.3 - Expand Your Knowledge: Estimating the Standard...Ch. 7.3 - Estimating the Standard Deviation: Refrigerator...Ch. 7.3 - Estimating the Standard Deviation: Veterinary...Ch. 7.3 - Estimating the Standard Deviation: Veterinary...Ch. 7.3 - Insurance: Satellites A relay microchip in a...Ch. 7.4 - Statistical Literacy What is a population? Give...Ch. 7.4 - Statistical Literac y What is a random sample from...Ch. 7.4 - Statistical Literacy What is a population...Ch. 7.4 - Statistical Literacy What is a sample statistic?...Ch. 7.4 - Statistical Literacy What is the meaning of the...Ch. 7.4 - Statistical Literacy What is a sampling...Ch. 7.4 - Critical Thinking How do frequency tables,...Ch. 7.4 - Critical Thinking How can relative frequencies be...Ch. 7.4 - Critical Thinking Give an example of a specific...Ch. 7.5 - Statistical Literacy What is the standard error of...Ch. 7.5 - Statistical Literacy What is the standard...Ch. 7.5 - Statistical Literacy List two unbiased estimators...Ch. 7.5 - Statistical Literacy Describe how the variability...Ch. 7.5 - Basic Computation: Central Limit Theorem Suppose x...Ch. 7.5 - Basic Computation: Central Limit Theorem Suppose x...Ch. 7.5 - Prob. 7PCh. 7.5 - Critical Thinking Suppose x has a distribution...Ch. 7.5 - Critical Thinking Consider two x distributions...Ch. 7.5 - Critical Thinking Consider an x distribution with...Ch. 7.5 - Critical Thinking Suppose x has a distribution...Ch. 7.5 - Critical Thinking Suppose an x distribution has...Ch. 7.5 - Coal: Automatic Loader Coal is carried from a mine...Ch. 7.5 - Vital Statistics: Heights of Men The heights of...Ch. 7.5 - Medical: Blood Glucose Let x be a random variable...Ch. 7.5 - Medical: White Blood Cells Let x be a random...Ch. 7.5 - Wildlife: Deer Let x be a random variable that...Ch. 7.5 - Focus Problem: Impulse Buying Let x represent the...Ch. 7.5 - Finance: Templeton Funds Templeton world is a...Ch. 7.5 - Finance: European Growth Fund A European growth...Ch. 7.6 - Statistical Literacy Binomial probability...Ch. 7.6 - Statistical Literacy When we use a normal...Ch. 7.6 - Basic Computation: Normal Approximation to a...Ch. 7.6 - Basic Computation: Normal Approximation to a...Ch. 7.6 - Critical Thinking You need to compute the...Ch. 7.6 - Critical Thinking Consider a binomial experiment...Ch. 7.6 - In the following problems, check that it is...Ch. 7.6 - Insurance: Claims Do you try to pad an insurance...Ch. 7.6 - Longevity: 90th Birthday It is estimated that 3.5%...Ch. 7.6 - Fishing: Billfish Ocean fishing for billfish is...Ch. 7.6 - Grocery Stores: New ProductsThe Denver Post slated...Ch. 7.6 - Crime: Murder What are the chances that a person...Ch. 7.6 - Supermarkets: Free Samples Do you take the free...Ch. 7.6 - Ice Cream: Flavors Whats your favorite ice cream...Ch. 7.6 - Airline Flights: No-Shows Based on long...Ch. 7.6 - 16. General: Approximations We have studied the...Ch. 7.6 - Statistical Literacy Under what conditions is it...Ch. 7.6 - Statistical Literacy What is the formula for the...Ch. 7.6 - Statistical Literacy Is p an unbiased estimator...Ch. 7.6 - Basic Computation: p Distribution Suppose we have...Ch. 7.6 - Basic Computation: p Distribution Suppose we have...Ch. 7 - Terminology Consider the graph of a normal...Ch. 7 - Terminology What are the values of the mean and...Ch. 7 - Terminology Answer the following statements...Ch. 7 - Terminology Consider all possible random samples...Ch. 7 - Statistical Literacy Describe a normal probability...Ch. 7 - Statistical Literacy According to the empirical...Ch. 7 - Statistical Literacy Random sample of size 9 is...Ch. 7 - Statistical Literacy Can a normal distribution...Ch. 7 - Statistical Literacy What characteristic of a...Ch. 7 - Statistical Liter acy For a normal distribution,...Ch. 7 - Statistical Literacy Give the formula for the...Ch. 7 - Statistical Literacy Give the formula for the...Ch. 7 - Critical Thinking Let x be a random variable...Ch. 7 - Critical Thinking If x has a normal distribution...Ch. 7 - Basic Computation: Probability Given that x is a...Ch. 7 - Basic Computation: Probability Given that x is a...Ch. 7 - Basic Computation: Inverse Normal Find z such that...Ch. 7 - Basic Computation: Inverse Normal Find z such that...Ch. 7 - Medical: Blood Type Blood type AB is found in only...Ch. 7 - Customer Complaints: Time The Customer Service...Ch. 7 - 21. Recycling: Aluminum Cans One environmental...Ch. 7 - 22. Guarantee: Battery Life Many people consider...Ch. 7 - Guarantee: Package Delivery Express Courier...Ch. 7 - Drugs: Effects A new muscle relaxant is available....Ch. 7 - Psychology: IQ Scores Assume that IQ scores are...Ch. 7 - Hatchery Fish: Length A large tank of fish from a...Ch. 7 - Basic Computation: p Distribution Suppose we have...Ch. 7 - Green Behavior: Purchasing Habits A recent Harris...Ch. 7 - Iris setosa is a beautiful wildflower that is...Ch. 7 - If you look up the word empirical in a dictionary,...Ch. 7 - Why are standard z values so important? Is it true...Ch. 7 - Most people would agree that increased information...Ch. 7 - In a way, the central limit theorem can be thought...
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- 11. (a) Define the (mathematical and conceptual) definition of conditional probability P(A|B).arrow_forward12. (a) Explain tail events and the tail o-field. Give an example.arrow_forwardLet A, A1, A2,... be measurable sets. Then P(A)=1- P(A); • P(Ø) = 0; P(A1 UA2) ≤ P(A1) + P(A2); A1 C A2 P(A1) P(A2); P(UA) + P(n=14) = 1. Exercise 3.1 Prove these relations. ☐arrow_forward
- 17. Suppose that X1, X2,..., Xn are random variables, such that E|xk| < ∞ for all k, and set Yn = max1arrow_forward6. Show that, for any random variable, X, and a > 0, L P(x < X ≤ x+a) dx = a. 2015arrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that (P(X ≤ x ≤ Y) - P(Y < x ≤ X))dx = E Y — E X.arrow_forward2. Which of the following statements are (not) true? lim sup{An U Bn} 818 lim sup{A, B} 818 lim inf{An U Bn} 818 818 lim inf{A, B} An An A, Bn- A, BnB →B = = = lim sup A, U lim sup Bn; 818 818 lim sup A, lim sup Bn; 818 81U lim inf A, U lim inf Bn; 818 818 lim inf A, lim inf Bn; n→X 818 An U BRAUB as no; An OBRANB as n→∞.arrow_forwardThroughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2. 1. Show that AAB (ANB) U (BA) = (AUB) (AB), Α' Δ Β = Α Δ Β, {A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).arrow_forward16. Show that, if X and Y are independent random variables, such that E|X|< ∞, and B is an arbitrary Borel set, then EXI{Y B} = EX P(YE B).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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