Sears rates its salespersons according to their sales ability and their potentia

Question

Sears rates its salespersons according to their sales ability and their potential for advancement. They sampled 500 salespeople with following data: Potential for Advancement Fair Good Excellent Below Average 16 12 22 Average 45 60 45 Above Average 93 72 135 (a) Calculate the probability that a randomly selected Sear's salesperson has above average sales ability and is an excellent potential for advancement? (b) Calculate the probability that a randomly selected Sear's salesperson will have average sales ability an and good potential for advancement? (c) Calculate the probability that a randomly selected Sear's salesperson will have below average sales ability and fair potential for advancement? (d) Calculate the probability that a randomly selected Sear's salesperson will have an excellent potential for advancement given they also have above average sales ability? (e) Calculate the probability that a randomly selected Sear's salesperson will have an excellent potential for advancement given they also have average sales ability?

Explanation / Answer

Below average sales person = 50
Average = 150
Above average = 300

P(below sales ) = 50/500 = 0.1
similarly P(average) = 0.3
P(above avg.) = 0.6

(A) 0.6 x 135/300 = 0.270
(B) 0.3 x 60/150 = 0.120
(C) 0.1 x 16/50 = 0.0320
(D) (135/500)/0.6 = 0.450
(E) (45/500)/0.3 = 0.300

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