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 month's results are reported in the following two-way frequency table.

No increase | Increased sales | |
---|---|---|

No Seminar |
25 |
35 |

Seminar |
63 |
77 |

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(increased sales) (b)Find the probability that the salesperson increased sales, given that she took the seminar. =P(increased sales | seminar) (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). 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). |

Answer #1

a) The probability that the salesperson increased sales is
computed here as:

P( increased sales)

= n(increased sales) / n(Total)

= (35 + 77) / 200

= 0.56

**Therefore 0.56 is the required probability
here.**

b) The probability that the salesperson increased sales, given
that she took the seminar is computed using Bayes theorem here
as:

P(increased sales | seminar) = n(increased sales and seminar) /
n(seminar)

= 77 / (77 + 63)

= 0.55

**Therefore 0.55 is the required probability
here.**

c) As the sales person who took the seminar has a probability of
0.55 of increased sales, and the probability in general for
increased sales is 0.56 approx. equal to 0.55, therefore
**No** **because the probability found in part
(b) is about the same as the probability found in part
(a)**

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