Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.
Potential for advancement | ||||
Fair | Good | Excellent | ||
Sales Ability | Below average | 16 | 12 | 22 |
Average | 45 | 60 | 45 | |
Above average | 93 | 72 | 135 |
a) What is the probability that a salesperson selected at random has above average sales ability?
b) What is the probability that a salesperson selected at random has an excellent potential for advancement?
c) What is the probability that a salesperson selected at random has above average sales ability and is an excellent potential for advancement?
d) What is the probability that a salesperson selected at random has above average sales ability, knowing that he/she has an excellent potential for advancement?
e) Are the events "a salesperson selected at random has above average sales ability" and "a salesperson selected at random has an excellent potential for advancement" independents?
Fair | Good | Excellent | Total | |
Belw average | 16 | 12 | 22 | 50 |
Average | 45 | 60 | 45 | 150 |
Above Average | 93 | 72 | 135 | 300 |
Total | 154 | 144 | 202 | 500 |
a)
P(Above Average) = 300/500 = 0.60
b)
P(Excellent) = 202/500 = 0.4040
c)
P(Above Average and Excellent) = 135/500 = 0.27
d)
P(Above Average | Excellent) = P(Above Average and Excellent) / P(Excellent)
= (135/500) / (202/500) = 0.6683
e)
No, these events are not independent.
As for independence P(A and B) = P(A)*P(B). It is not true in this case.
Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement
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