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Chapter 7.5, Problem 18P

Focus Problem: Impulse Buying Let x represent the dollar Amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a Denever post article, the mean of the x distribution is about $20 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 100 customers, each of whom has

10 minutes of unplanned shopping time in a supermarket. Rom the central limit theorem, what can you say about the probability distribution of x ¯ , the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x ¯ distribution? Is it necessary to make any assumption about the x distribution ? Explain.

(b) What is the probability that x ¯ is between $18 and $22?

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $18 and $22?

(d) Interpretation In part (b), we used x ¯ . the average amount spent, computed for 100 customers. In part (c). we used x, the amount spent by only one customer. The answers to pans (b) and (c) are very different. Why would this happen? In this example. x ¯ is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

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Chapter 7 Solutions

Bundle: Understanding Basic Statistics, Loose-leaf Version, 7th + WebAssign Printed Access Card for Brase/Brase's Understanding Basic Statistics, ... for Peck's Statistics: Learning from Data

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 - Prob. 11PCh. 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 - 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 - Prob. 18CRCh. 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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