EBK STATISTICS FOR ENGINEERS AND SCIENT
4th Edition
ISBN: 9780100274389
Author: Navidi
Publisher: YUZU
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Textbook Question
Chapter 2.2, Problem 7E
A test consists of 15 questions. Ten are true-false questions, and five are multiple-choice questions that have four choices each. A student must select an answer for each question. In how many ways can this be done?
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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.
Chapter 2 Solutions
EBK STATISTICS FOR ENGINEERS AND SCIENT
Ch. 2.1 - The probability that a bearing fails during the...Ch. 2.1 - A die (six faces) has the number 1 painted on...Ch. 2.1 - A section of an exam contains four True-False...Ch. 2.1 - Three times each day, a quality engineer samples a...Ch. 2.1 - Four candidates are to be interviewed for a job....Ch. 2.1 - Refer to Exercise 5. Two candidates are randomly...Ch. 2.1 - In a survey of households with television sets,...Ch. 2.1 - An automobile insurance company divides customers...Ch. 2.1 - Among the cast aluminum parts manufactured on a...Ch. 2.1 - The article High Cumulative Risk of Lung Cancer...
Ch. 2.1 - A quality-control engineer samples 100 items...Ch. 2.1 - Let V be the event that a computer contains a...Ch. 2.1 - Let S be the event that a randomly selected...Ch. 2.1 - Six hundred paving stones were examined for...Ch. 2.1 - All the fourth-graders in a certain elementary...Ch. 2.1 - A system contains two components, A and B. The...Ch. 2.1 - A system contains two components, A and B. The...Ch. 2.1 - Human blood may contain either or both of two...Ch. 2.1 - True or false: If A and B are mutually exclusive,...Ch. 2.1 - A flywheel is attached to a crankshaft by 12...Ch. 2.2 - DNA molecules consist of chemically linked...Ch. 2.2 - A metallurgist is designing an experiment to...Ch. 2.2 - The article Improved Bioequivalence Assessment of...Ch. 2.2 - A group of 18 people have gotten together to play...Ch. 2.2 - In horse racing, one can make a trifecta bet by...Ch. 2.2 - A college math department consisting of 10 faculty...Ch. 2.2 - A test consists of 15 questions. Ten are...Ch. 2.2 - In a certain state, license plates consist of...Ch. 2.2 - A computer password consists of eight characters....Ch. 2.2 - A company has hired 15 new employees, and must...Ch. 2.2 - Let A and B be events with P(A) = 0.8 and P(A B)...Ch. 2.2 - A drawer contains 6 red socks, 4 green socks, and...Ch. 2.3 - Let A and B be events with P(A) = 0.8 and P(A B)...Ch. 2.3 - Let A and B be events with P(A) = 0.5 and P(A Bc)...Ch. 2.3 - A box contains 15 resistors. Ten of them are...Ch. 2.3 - Prob. 4ECh. 2.3 - On graduation day at a large university, one...Ch. 2.3 - The article Integrating Risk Assessment and Life...Ch. 2.3 - Suppose that start-up companies in the area of...Ch. 2.3 - A drag racer has two parachutes, a main and a...Ch. 2.3 - Of people in a certain city who bought a new...Ch. 2.3 - Of all failures of a certain type of computer hard...Ch. 2.3 - In the process of producing engine valves, the...Ch. 2.3 - Sarah and Thomas are going bowling. The...Ch. 2.3 - A particular automatic sprinkler system has two...Ch. 2.3 - Laura and Philip each fire one shot at a target....Ch. 2.3 - A population of 600 semiconductor wafers contains...Ch. 2.3 - Refer to Exercise 15. Let E1 be the event that the...Ch. 2.3 - A geneticist is studying two genes. Each gene can...Ch. 2.3 - A car dealer sold 750 automobiles last year. The...Ch. 2.3 - The following table presents the 100 senators of...Ch. 2.3 - An automobile insurance company divides customers...Ch. 2.3 - Nuclear power plants have redundant components in...Ch. 2.3 - Prob. 22ECh. 2.3 - A lot of 10 components contains 3 that are...Ch. 2.3 - A lot of 1000 components contains 300 that are...Ch. 2.3 - In a lot of n components, 30% are defective. Two...Ch. 2.3 - Prob. 26ECh. 2.3 - Each day, a weather forecaster predicts whether or...Ch. 2.3 - Items are inspected for flaws by two quality...Ch. 2.3 - Refer to Exercise 28. Assume that both inspectors...Ch. 2.3 - Refer to Example 2.26. Assume that the proportion...Ch. 2.3 - Sickle-cell anemia is an inherited disease in...Ch. 2.3 - A quality-control program at a plastic bottle...Ch. 2.3 - Refer to Example 2.26. a. If a man tests negative,...Ch. 2.3 - A system consists of four components connected as...Ch. 2.3 - A system consists of four components, connected as...Ch. 2.3 - A system contains two components, A and B,...Ch. 2.3 - A system contains two components, C and D,...Ch. 2.3 - If A and B are independent events, prove that the...Ch. 2.4 - Determine whether each of the following random...Ch. 2.4 - Computer chips often contain surface...Ch. 2.4 - A chemical supply company ships a certain solvent...Ch. 2.4 - Let X represent the number of tires with low air...Ch. 2.4 - A survey of cars on a certain stretch of highway...Ch. 2.4 - The element titanium has five stable occurring...Ch. 2.4 - A computer sends a packet of information along a...Ch. 2.4 - After manufacture, computer disks are tested for...Ch. 2.4 - On 100 different days, a traffic engineer counts...Ch. 2.4 - Microprocessing chips are randomly sampled one by...Ch. 2.4 - Refer to Exercise 10. Let Y be the number of chips...Ch. 2.4 - Three components are randomly sampled, one at a...Ch. 2.4 - Resistors labeled 100 have true resistances that...Ch. 2.4 - Elongation (in percent) of steel plates treated...Ch. 2.4 - The lifetime in months of a transistor in a...Ch. 2.4 - A process that manufactures piston rings produces...Ch. 2.4 - Refer to Exercise 16. A competing process produces...Ch. 2.4 - The lifetime, in years, of a certain type of pump...Ch. 2.4 - The level of impurity (in percent) in the product...Ch. 2.4 - The main bearing clearance (in mm) in a certain...Ch. 2.4 - The error in the length of a part (absolute value...Ch. 2.4 - Prob. 22ECh. 2.4 - The thickness of a washer (in mm) is a random...Ch. 2.4 - Particles are a major component of air pollution...Ch. 2.4 - The repair time (in hours) for a certain machine...Ch. 2.4 - The diameter of a rivet (in mm) is a random...Ch. 2.5 - Prob. 1ECh. 2.5 - The bottom of a cylindrical container has an area...Ch. 2.5 - The lifetime of a certain transistor in a certain...Ch. 2.5 - Two batteries, with voltages V1 and V2, are...Ch. 2.5 - A laminated item is composed of five layers. The...Ch. 2.5 - Two independent measurements are made of the...Ch. 2.5 - The molarity of a solute in solution is defined to...Ch. 2.5 - A machine that fills bottles with a beverage has a...Ch. 2.5 - The four sides of a picture frame consist of two...Ch. 2.5 - A gas station earns 2.60 in revenue for each...Ch. 2.5 - A certain commercial jet plane uses a mean of 0.15...Ch. 2.5 - Prob. 12ECh. 2.5 - In the article An Investigation of the...Ch. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - The thickness X of a wooden shim (in mm) has...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.6 - In a certain community, levels of air pollution...Ch. 2.6 - Prob. 2ECh. 2.6 - Refer to Exercise 1. a. Find the conditional...Ch. 2.6 - Prob. 4ECh. 2.6 - Refer to Exercise 4. The total number of...Ch. 2.6 - Refer to Exercise 4. a. Find the conditional...Ch. 2.6 - Refer to Exercise 4. Assume that the cost of...Ch. 2.6 - The number of customers in line at a supermarket...Ch. 2.6 - Prob. 9ECh. 2.6 - Refer to Exercise 9. a. Find the mean of the total...Ch. 2.6 - Refer to Exercise 9. a. Find the conditional...Ch. 2.6 - Prob. 12ECh. 2.6 - Refer to Exercise 12. Let Z = X + Y represent the...Ch. 2.6 - Refer to Exercise 12. Assume that the cost of an...Ch. 2.6 - Automobile engines and transmissions are produced...Ch. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - A production facility contains two machines that...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - The lifetime of a certain component, in years, has...Ch. 2.6 - Prob. 22ECh. 2.6 - An investor has 100 to invest, and two investments...Ch. 2.6 - Prob. 24ECh. 2.6 - Let R denote the resistance of a resistor that is...Ch. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Let X and Y be jointly distributed random...Ch. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2 - A system consists of four components connected as...Ch. 2 - A fair coin is tossed until a head appears. What...Ch. 2 - Silicon wafers are used in the manufacture of...Ch. 2 - Two production lines are used to pack sugar into 5...Ch. 2 - Prob. 5SECh. 2 - In a certain type of automobile engine, the...Ch. 2 - An electronic message consists of a string of bits...Ch. 2 - The reading given by a thermometer calibrated in...Ch. 2 - Two dice are rolled. Given that two different...Ch. 2 - In a lot of 10 components, 2 are sampled at random...Ch. 2 - Prob. 11SECh. 2 - Prob. 12SECh. 2 - A snowboard manufacturer has three plants, one in...Ch. 2 - The article Traps in Mineral ValuationsProceed...Ch. 2 - Six new graduates are hired by an engineering...Ch. 2 - Prob. 16SECh. 2 - Let X and Y be independent random variables with x...Ch. 2 - Prob. 18SECh. 2 - Prob. 19SECh. 2 - Prob. 20SECh. 2 - Prob. 21SECh. 2 - A certain plant runs three shifts per day. Of all...Ch. 2 - Prob. 23SECh. 2 - Prob. 24SECh. 2 - Prob. 25SECh. 2 - A stock solution of hydrochloric acid (HC1)...Ch. 2 - Prob. 27SECh. 2 - Prob. 28SECh. 2 - A penny and a nickel are tossed. The penny has...Ch. 2 - Prob. 30SECh. 2 - Prob. 31SECh. 2 - Prob. 32SECh. 2 - Prob. 33SECh. 2 - Prob. 34SECh. 2 - Blood is taken from each of n individuals to be...
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