Question

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.

\

$$\begin{tabular}{|c|c|c|} \\hline & increased sales & no increase \\\\ \\hline seminar & 78 & 26 \\\\ \\hline no seminar & 24 & 72 \\\\ \\hline \\end{tabular}$$

a salesperson is chosen at random from this group.
complete the following. write your answers as decimals.

(a) find the probability that the salesperson increased sales.
\\(p(\text{increased sales}) = \square\\)

(b) find the probability that the salesperson increased sales, given that she took the seminar.
\\(p(\text{increased sales} \mid \text{seminar}) = \square\\)

(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?
\\(\bigcirc\\) yes, because the probability found in part (b) is much greater than the probability found in part (a).
\\(\bigcirc\\) no, because the probability found in part (b) is much greater than the probability found in part (a).
\\(\bigcirc\\) yes, because the probability found in part (a) is much greater than the probability found in part (b).
\\(\bigcirc\\) no, because the probability found in part (a) is much greater than the probability found in part (b).
\\(\bigcirc\\) yes, because the probability found in part (b) is about the same as the probability found in part (a).
\\(\bigcirc\\) no, because the probability found in part (b) is about the same as the probability found in part (a).

Explanation:

Calculate the probability of increased sales

$$
LATEXBLOCK0
$$

Calculate the conditional probability given seminar

$$
LATEXBLOCK1
$$

Compare probabilities for evidence

$$
LATEXBLOCK2
$$

Answer:

Question (a)

Find the probability that the salesperson increased sales.
P(increased sales) = <blank>0.51</blank>

Question (b)

Find the probability that the salesperson increased sales, given that she took the seminar.
P(increased sales | seminar) = <blank>0.75</blank>

Question (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?

• Yes, because the probability found in part (b) is much greater than the probability found in part (a). (Correct answer)
• No, because the probability found in part (b) is much greater than the probability found in part (a).
• Yes, because the probability found in part (a) is much greater than the probability found in part (b).
• No, because the probability found in part (a) is much greater than the probability found in part (b).
• Yes, because the probability found in part (b) is about the same as the probability found in part (a).
• No, because the probability found in part (b) is about the same as the probability found in part (a).