EBK BUSINESS ANALYTICS
3rd Edition
ISBN: 9780136880844
Author: Evans
Publisher: PEARSON
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Chapter 5, Problem 6PE
Refer to the card scenario described in Problem 3.
- Let A be the
event "total card value is odd." Findprobability that the sum of the two cards will be more than - What is the probably that the sum of the two cards will not exceed
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 5 Solutions
EBK BUSINESS ANALYTICS
Ch. 5 - Lauren drinks a variety of soft drinks. Over the...Ch. 5 - A home improvement company in Cincinnati ran a...Ch. 5 - Consider the experiment of drawing two cards...Ch. 5 - Three coins are drop on a table. List all possible...Ch. 5 - A market research company surveyed consumers to...Ch. 5 - Refer to the card scenario described in Problem 3....Ch. 5 - Refer to the coin scenario described in Problem 4....Ch. 5 - Prob. 8PECh. 5 - Prob. 9PECh. 5 - An airline tracks data on its flight arrivals....
Ch. 5 - A survey of 200 college graduates who have been...Ch. 5 - Prob. 12PECh. 5 - A survey of shopping habits found the percentage...Ch. 5 - A Canadian business school summarized the gender...Ch. 5 - Prob. 15PECh. 5 - Use the Civilian Labor Force data in the Excel...Ch. 5 - Prob. 17PECh. 5 - A home pregnancy test is not always accurate....Ch. 5 - In the scenario in Problem 3, what is the...Ch. 5 - In the roulette example described in Problem 8,...Ch. 5 - Prob. 21PECh. 5 - An investor estimates that there is a 1in10 chance...Ch. 5 - The weekly demand of a slow-moving product has the...Ch. 5 - Construct the probability distribution for the...Ch. 5 - Based on the data in the Excel file Consumer...Ch. 5 - A major application of analytics in marketing is...Ch. 5 - The Excel file Call Center Data shows that in a...Ch. 5 - If a cell phone company conducted a telemarketing...Ch. 5 - During one year, a particular mutual fund...Ch. 5 - A popular resort hotel has 300 rooms and is...Ch. 5 - A telephone call center where people place...Ch. 5 - A financial consultant has an average of eight...Ch. 5 - The number and frequency of Atlantic hurricanes...Ch. 5 - Prob. 34PECh. 5 - Prob. 35PECh. 5 - Prob. 36PECh. 5 - In determining automobile mileage ratings, it was...Ch. 5 - The distribution of SAT scores in math for an...Ch. 5 - A popular soft drink is sold in 2-liter...Ch. 5 - A supplier contract calls for a key dimension of a...Ch. 5 - Historical data show that customers who download...Ch. 5 - A lightbulb is warranted to last for 5,000 hours....Ch. 5 - The actual delivery time from Giodannis Pizza is...Ch. 5 - Apply the chi-square goodness of fit test to the...Ch. 5 - Apply the chi-square goodness of fit test to the...Ch. 5 - Compute the daily change of the closing price for...
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