Question

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? 

Answer 1

Answer 2

5. Giren the table #demoes "number of a) Probability that a salespension selected at randon has above average sates ability. pro PCAA) #people with above average sates ability # total people 93+72+ 135 500 300 500 0.6 b) Probability that a salesperson selected at random has an excellent potontal for advancement = P(E) #people with excellent potential for advancement #total people 22+45+135 202 10.904 500 500 c) Probability that salesperson has are above average sales ability and is an excellent potenital for advancement = BCAA PAA nEO) # people with above average salgs ability of and excellent potential for advancement #total people 135 500 d) Probality that a salespenson has above average sales ability knowing that he/she has an excellent potenital for advancement - PCAALE) and # people having above average sales ability green that he/she has an excellent potential for advancement # people with excellent potential for advancement

Answer 3

	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.

Answer 4

5. Giren the table #demoes "number of a) Probability that a salespension selected at randon has above average sates ability. pro PCAA) #people with above average sates ability # total people 93+72+ 135 500 300 500 0.6 b) Probability that a salesperson selected at random has an excellent potontal for advancement = P(E) #people with excellent potential for advancement #total people 22+45+135 202 10.904 500 500 c) Probability that salesperson has are above average sales ability and is an excellent potenital for advancement = BCAA PAA nEO) # people with above average salgs ability of and excellent potential for advancement #total people 135 500 d) Probality that a salespenson has above average sales ability knowing that he/she has an excellent potenital for advancement - PCAALE) and # people having above average sales ability green that he/she has an excellent potential for advancement # people with excellent potential for advancement

0.668 135 202 Now CC e) for the events AA & F to be independent PCAA QE) A PCAA). PCE) must hold frie De means almost equal. Here PCAANE) = 0.27. PCAA). PCE): 0.2424 Clearly, there are not close enough So, events sales penson selected at random has sales ability, and ai salesperson selected at random has an excellent potenital for improvement" are are not independent 11n above average of (432) با پودر کارینا