the sales for each of 200 salespeople were recorded one month. then some of the salespeople took a sales…

the sales for each of 200 salespeople were recorded one month. then some of the salespeople took a sales training seminar and the rest did not. the next months results are reported in the following two - way frequency table.\n| |no increase|increased sales|\n|--|--|--|\n|no seminar|29|31|\n|seminar|63|77|\na salesperson is chosen at random from this group. complete the following. write your answers as decimals.\n(a) find the probability that the salesperson increased sales. p(increased sales) = \n(b) find the probability that the salesperson increased sales, given that she took the seminar. p(increased sales | seminar) = \n(c) is there evidence that a salesperson who takes the seminar is more likely to increase sales than a randomly chosen salesperson from the group?\nyes, because the probability found in part (b) is much greater than the probability found in part (a).\nno, because the probability found in part (b) is much greater than the probability found in part (a).\nyes, because the probability found in part (a) is much greater than the probability found in part (b).\nno, because the probability found in part (a) is much greater than the probability found in part (b).\nyes, because the probability found in part (b) is about the same as the probability found in part (a).\nno, because the probability found in part (b) is about the same as the probability found in part (a).

the sales for each of 200 salespeople were recorded one month. then some of the salespeople took a sales training seminar and the rest did not. the next months results are reported in the following two - way frequency table.\n| |no increase|increased sales|\n|--|--|--|\n|no seminar|29|31|\n|seminar|63|77|\na salesperson is chosen at random from this group. complete the following. write your answers as decimals.\n(a) find the probability that the salesperson increased sales. p(increased sales) = \n(b) find the probability that the salesperson increased sales, given that she took the seminar. p(increased sales | seminar) = \n(c) is there evidence that a salesperson who takes the seminar is more likely to increase sales than a randomly chosen salesperson from the group?\nyes, because the probability found in part (b) is much greater than the probability found in part (a).\nno, because the probability found in part (b) is much greater than the probability found in part (a).\nyes, because the probability found in part (a) is much greater than the probability found in part (b).\nno, because the probability found in part (a) is much greater than the probability found in part (b).\nyes, because the probability found in part (b) is about the same as the probability found in part (a).\nno, because the probability found in part (b) is about the same as the probability found in part (a).

Answer

Explanation:

Step1: Calculate total number of salespeople

The total number of sales - people is (29 + 31+63 + 77=200).

Step2: Calculate probability of increased sales (a)

The number of salespeople with increased sales is (31 + 77 = 108). So (P(\text{increased sales})=\frac{31 + 77}{29+31 + 63+77}=\frac{108}{200}=0.54).

Step3: Calculate probability of increased sales given took seminar (b)

The number of salespeople who took the seminar is (63 + 77 = 140), and the number of those who took the seminar and increased sales is (77). So (P(\text{increased sales}|\text{seminar})=\frac{77}{63 + 77}=\frac{77}{140}=0.55).

Step4: Analyze the results (c)

Since (P(\text{increased sales}|\text{seminar}) = 0.55) and (P(\text{increased sales})=0.54), and (0.55) is slightly greater than (0.54), a sales - person who takes the seminar is more likely to increase sales.

Answer:

(a) (0.54) (b) (0.55) (c) Yes, because the probability found in part (b) is much greater than the probability found in part (a).