In the evaluation of its sales training program, a firm discovered that out of 5
ID: 3072625 • Letter: I
Question
In the evaluation of its sales training program, a firm discovered that out of 50 people receiving a bonus last year, 20 had attended a special sales training program. The firm has 200 sales people and 40% of the firm's salespeople have attended the training program. The contingency table associated with this case is as follow:
A. Find the probability that a salesperson chosen at random has received a bonus.
B. Find the probability that a salesperson chosen at random has attended the training program given that he or she received a bonus.
C. Find the probability that a salesperson makes a bonus given that he or she attended the sales training program.
D. Are the events of attending the training program and receiving a bonus independent? Support your response with appropriate computations.
E. Based on your computations, do you think the training program is effective in helping employees to receive a bonus? Explain.
Received Bonus Did not Receive Bonus Total Attended Training Program 20 60 80 Did not Attend Training 30 90 120 Total 50 150 200Explanation / Answer
a) P(Received bonus) = 50/200 = 0.25
b) P(Attended the training program | Bonus) = 20/50 = 0.40
c) P(Bonus | Attended the training program) = 20/80 = 0.25
d) P(Attended the training program and received bonus) = 20/200 = 0.10
P(Attended the training program) = 80/200 = 0.40
P(Bonus) = 50/200 = 0.25
So,
P(Attended the training program)*P(Bonus) = 0.40*0.25 = 0.10
Since P(Attended the training program and received bonus) = P(Attended the training program)*P(Bonus), these two events are independent.
e) Since these two events are independent, it doesn't seem like the training program is effective in helping employees to receive a bonus.