Question

SELF 4.24 What business and technical skills are critical Test for today's business intelligence/analytics and infor- mation management professionals? As part of InformationWeek's 2013 U.S. IT Salary Survey, business intelligence/analytics and information management professionals, both staff and managers were asked to indicate what business and technical skills are criti- cal to their job. The list of business and technical skills included Analyzing Data. The following table summarizes the responses to this skill: k. ity the hat PROFESSIONAL POSITION act- Management Total ANALYZING DATA Staff ared um 8.007 3.633 2.631 4,374 Critical 6.067 Not critical 3.436 7.810 898 14.074 6.264 Total Source: Data extracted from "TT Salanes Show Slow Growth. Information Week Reports April 2013, p. 40. ubmio/lewjKTS. professional is staff, what is the probability that a Given tha the professional indicates analyzing data as critical to his or her job? b. Given that a professionall is staff, what is the probability that the professional does not indicate analyzing data as critical to his or her job? Given that a professional is a manager, what is the probability that the professional indicates analyzing data as critical to his or her job? d. Given thata professional is a manager, what is the probability that the professional does not indicate analyzing data as critical to his or her job? a S keter use of rketer use of s focus, 準197自3 4.25 A survey of 1,085 adults asked, "Do you enjoy shopping for clothing for yourself?" The results (data extracted from "Split De- cision on Clothes Shopping," USA Today. January 28, 2011, p. 1B) indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 44% of the males. The sample sizes of males and females were not provided. Suppose that the results were as shown in the following table: GENDER ENJOYS SHOPPING FOR CLOTHING Female Male Total 276 514 Yes 238 571 No 304 267 543 Total 542 1,085 Suppose that the respondent chosen is a female. What is the probability that she does not enjoy shopping for clothing? b. Suppose that the respondent chosen enjoys shopping for clothing. What is the probability that the individual is a male? C. Are enjoying shopping for clothing and the gender of the individual independent? Explain a. 4.26 Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty- related repair (yes or no) and the country in which the company manufacturing a car is based (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufac- tured by a U.S.-based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S.- based company is 0.025. a. Suppose you know that a company based in the United States manufactured a particular car. What is the probability that the car needs a warranty repair? b. Suppose you know that a company based in the United States did not manufacture a particular car. What is the probability that the car needs a warranty repair? c. Are need for a warranty repair and location of the company manufacturing the car independent? 4.27 In 40 of the 62 years from 1950 through 2012 (in 2011 there was virtually no change), the S&P 500 finished higher after the first five days of trading. In 35 of those 40 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 62-year period: 169 4.3 Bayes' Theorem S&P 500'S ANNUAL PERFORMANCE Higher Lower FIRST WEEK 5 35 Higher Lower 1 11 a. If a year is selected at random, what is the probability that the S&P 500 finished higher for the year? b. Given that the S&P 500 finished higher after the first five days of trading, what is the probability that it finished higher for the year? c. Are the two events "first-week performance" and "annual per- formance" independent? Explain. d. Look up the performance after the first five days of 2013 and the 2013 annual performance of the S&P 500 at finance.yahoo.com Comment on the results. 4.28 A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs, and spades), each having 13 faces (ace, 2, 3, 4, 5,6, 7, 8,9, 10, jack, queen, and king), making total of 52 cards. This complete deck is thoroughly mixed, and you will receive the first 2 cards from the deck, without replacement (the first card is not returned to the deck after it is selected). a. What is the probability that both cards are queens? b. What is the probability that the first card is a 10 and the second card is a 5 or 6? c. If you were sampling with replacement (the first card is returned to the deck after it is selected), what would be the answer in (a)? d. In the game of blackjack, the face cards (jack, queen, king) count as 10 points, and the ace counts as either 1 or 11 points. All other cards are counted at their face value. Blackjack is achieved if 2 cards total 21 points. What is the probability of getting blackjack in this problem? 4.29 A box of nine gloves contains two left-handed gloves and seven right-handed gloves. a. If two gloves are randomly selected from the box, without re- placement (the first glove is not returned to the box after it is selected), what is the probability that both gloves selected will be right-handed? b. If two gloves are randomly selected from the box, without re- placement (the first glove is not returned to the box after it is selected), what is the probability that there will be one right- handed glove and one left-handed glove selected? c. If three gloves are selected, with replacement (the gloves are returned to the box after they are selected), what is the prob- ability that all three will be left-handed? d. If you were sampling with replacement (the first glove is returned to the box after it is selected), what would be the answers to (a) and (b)? loulotad probabilities based on new informa-

Answer 1

4.24:(a)

Out of 7810 staff, 4374 think analyzing data critical to his or her job so

P(critical | staff) = 4374 / 7810 = 0.5601

(b)

P(not critical | staff) = 1 - P(critical | staff) = 1 - 0.5601 = 0.4399

(c)

Out of 6264 managers, 3633 think analyzing data critical to his or her job so

P(critical | staff) = 3633 / 6264 = 0.5800

(d)

P(not critical | staff) = 1 - P(critical | staff) = 1 - 0.5800 = 0.4200