Please complete the following problems in a Word document. Each problem is worth 3 points. Chapter 4: 12, 14, 40
Chapter 5: 10, 22, 28
Chapter 6: 6, 16, 20, 24
12. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then select five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through 42. To determine the winning numbers for each game, lottery officials draw five white balls out of a drum with 55 white balls, and one red ball out of a drum with 42 red balls. To win the jackpot, a participant’s numbers must match the numbers on the five white balls in any order and the number on the red Powerball. Eight coworkers at the ConAgra Foods plant in Lincoln, Nebraska, claimed the record $365 million jackpot on February 18, 2006, by matching the numbers 15-17-43-44-49 and the Powerball number 29. A variety of other cash prizes are awarded each time the game is played. For instance, a prize of $200,000 is paid if the participant’s five numbers match the numbers on the five white balls (www.powerball.com, March 19, 2006). a. Compute the number of ways the first five numbers can be selected.
The first 5 numbers can be selected in 3,478,761 ways
b. What is the probability of winning a prize of $200,000 by matching the numbers on the five white balls? The probability of winning the $200,000 prize is since the outcomes of an equal probability of winning
c. What is the probability of winning the Powerball jackpot? The Probability of winning the Jackpot is
14. An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E2 occurs?
b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)?
The probability that any two of the outcomes occur is .
c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?
The probability that any three of the outcomes occur is .
40. The prior probabilities for events A1, A2, and A3are P(A1) # .20, P(A2) # .50, and P(A3) # .30. The conditional probabilities of event B given A1, A2, and A3 are P(B ' A1) # .50, P(B ' A2) # .40, and P(B ' A3) # .30.
a. Compute P(B $ A1), P(B $ A2), and P(B $ A3).
b. Apply Bayes’ theorem, equation (4.19), to compute the posterior probability P(A2 ' B).
c. Use the tabular approach to applying Bayes’ theorem to compute P(A1 ' B), P(A2 ' B), and P(A3 ' B).
10. Table 5.4 shows the percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
a. Develop a probability distribution for the job satisfaction score of a senior executive.
IS Score (x)
IS Senior Executives %
b. Develop a probability distribution for the job satisfaction score of a middle manager.
IS Score (x)
IS Middle Managers %
c. What is the probability a senior executive will report a job satisfaction score of 4 or 5?
d. What is the probability a middle manager is very satisfied?
e. Compare the overall job satisfaction of senior executives and middle managers.
There are more senior Executives than Middle Managers that are highly satisfied
22. The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand....
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