Complete the following problems, and submit in pdf format (this can be generated from Microsoft Word). The purpose of this assignment is not merely to demonstrate your ability to make necessary calculations. The point is to demonstrate your ability to communicate important quantitative information to a well-informed reader. Number your answers in the document with the corresponding numbers in this assignment.
1. Michael Connelly has written two best-selling novels in the past year: Chasing the Dime, and City of Bones. Amazon.com has found that 4% of total purchasers of books ordered Chasing the Dime and 6% City of Bones. Given that they ordered Chasing the Dime, 60% also ordered City of Bones. a) What percentage ordered both novels? b) What percentage ordered neither book? c) Given that a customer did not buy Chasing the Dime, what percentage nonetheless did order City of Bones?
2. To reduce theft, the Meredeth Company screens all its employees for drug use with a urine test that is known to be correct 90 percent of the time (for both drug users and those who are not). George Meredeth decides to re all employees who fail the test. Suppose 5 percent of the employees are actually drug users. What do you think of George's policy?
3. Of your customers, 24% have high income, 17% are well educated. Furthermore, 12% are both high income and well educated. What percentage of the well-educated customers have high income? What does this tell you about a marketing eort that is currently reaching well-educated people although you would really prefer to high-income people?
4. Clinical trials of two drugs, Drug A and Drug B, are conducted. In trial 1, 200 people are given Drug A, and 40 are cured. Drug B is given to 200 people, and only 30 are cured. In trial 2, 100 people are given Drug A, and 85 are cured. Drug B is given to 400 people, and this time 300 are cured. Which drug is better?
5. Data on annual salaries of management personnel are taken from 100 men and 100 women. The mean salary for men was $53,000; the mean salary for women was $42,000. Among the lower-level management personnel, there were 10 men with a mean salary of $35,000 and 90 women with a mean salary of $40,000. Among the upper-level management personnel, there were 90 men with a mean salary of $55,000 and 10 women with a mean salary of $60,000. The data are summarized in the table below:
men women n mean n mean lower-level 10 35,000 90 40,000 upper-level 90 55,000 10 60,000 total 100 53,000 100 42,000
Who has the higher average salaries, men or women?
6. Consider the following (true) table from the National College Board, which shows verbal and math SAT scores in 1992 and 2002, by high school grade average:
percentage of students SAT scores High School in each grade average Verbal Math Grade avge 1992 2002 1992 2002 1992 2002 A+ 5% 7% 619 607 629 626 A 12 17 575 565 583 582 A- 14 17 546 538 554 553 B 52 47 486 479 486 485 C 17 11 434 424 428 424 all grades 100% 100% 500 504 501 516
Write a brief report describing any trends in SAT scores.
7. The following table represents the probability distributions of the prots from three dif- ferent proposals: Project A, Project B, and Project C:
Project A Project B Project C X P(X) X P(X) X P(X) 1000 .20 -5000 .20 -1000 .30 5000 .20 4000 .20 10000 .60 6000 .30 7000 .30 9000 .10 8000 .20 10000 .20 9000 .10 15000 .10
Evaluate the proposals in terms of expected prot and risk (measured by standard devia- tion).
8. A researcher is interested in conducting a mail survey. He nds out that there is a 10% rate of response to such questionnaires. If a questionnaire is mailed to 3 people, what is the probability a) that all respond? b) none respond?
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c) exactly one responds? d) at least one responds? e) at least two respond?
9. Suppose the manufacture of a product involves the assembly of six components. The probability that any single component is defective is only 0.05. If one or more components are defective, the product is defective. What proportion of the products produced will be defective?
10. Customers come through a check-out line an average of 5 per hour. What is the probability that in a given hour a) no customers come through the line b) at least 4 customers come through the line
11. The number of misprints for a daily newspaper averages 3.0 per page. What is the prob- ability of examining 3 pages at random and nding no misprints?
12. The lifetime of a particular component is normally distributed with a mean of 1,000 hours and a standard deviation of 100 hours. a) Find the probability that the component will last i. between 1,000 and 1,150 hours ii. between 950 and 1,000 hours iii. 1,070 hours or less iv. 930 hours or less v. more than 1,250 hours vi. between 700 and 1,200 hours vii. between 950 and 1,050 hours b) What is the 80th percentile of component lifetimes? c) What is the 30th percentile of component lifetimes? d) If a random sample of 9 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050? e) If a random sample of 25 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050? f) If a random sample of 100 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050?