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5.12. The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for slightly higher pay. In addition, 88% of companies say that there s a shortage of qualin ed job an dates. Suppose 6 workers are randomly selected and asked if they would change jobs for slightly higher pay. a. What is the probability that nine or more say yes? b. What is the probability that three, four, five, or six say yes? c. If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates? d. If 13 companies are contacted, what is the probability that all of the companies say there is a shortage of qualified job candidates? e. If 13 companies are contacted, what is the expected number of companies that would say there is a shortage of qualified job candidates?

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40% of the workers say they will change job for slightly higher pay n = number of workers selected = 16 Let p probability of a worker selected saying he/she would change job for slightly higher pay p 0.40 Let X be the number of workers who say they will change job for slightly higher pay Then X Binomial (n 16 and p 0.4) PDF of X is given by 40% f(x)-P(…)-() (0.4)(1-04)16-r where x = 0,1,2,3 a) To find probability that 9 or more say yes that is to find P(X 2 9) P(X29)-1-P(X 8) 9)-1 Σ(2 ) (0.4)(1-04)16-4 We use Excel function BINOM.DIST to find cumulative probability from 0 to 8 P(X 2 9) -1 BINOM.DIST(8,16,0.4,TRUE) = 0.1423 P(9 or more say yes) 0.1423 b) To find probability that 3,4,5 or 6 say yes that is to find P(X = 3) + P(x-4) + P(X = 5) + P(X = 6) P(X - 3,4,5,6)- ( 16 . (16 3) (0.4)*1-0.4)16-3+ (4(0.4)3-04)164 004)6-5+(6)(04s-04)6 16-6 0.04680.1014 0.16230.1983 0.5088 P(3,4,5 or 6 say yes) 0.5088c) Let X be the number of companies which say there is a shortage of qualified candidates n number of companies selected 13 Then X Binomial (n - 13 and p 0.88) PDF of X is given by 88% companies say there is a shortage fx)-P)(13) (0.88)*(1- 0.88)13- where x 0,1,2,3,...13 To find P(exactly 10 say there is shortage) that is to find P(X-10) P(X - 10) -( 0.88)10 (1- 0.88)13-10 - 0.1376 P(exactly 10 say there is shortage) 0.1376 d) To find P(all of the companies say there is shortage) that is to find P(X-13) P(X-13)-() (088)13(1-0.88)13-13 0.1898 P(all of the companies say there is shortage)-0.1898 e) As seen above, X follows binomial distribution where X be the number of companies which say there is a shortage of qualified candidates PDF of X is given by f(x) P(X х) ( 13 ) (0.88)(1-0.88)13-x where x-0,1,2,3, 13 Expectation of the binomial distribution is n*p 13*0.88 11.44 Expected number of companies that would say there is a shortage 11.44

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