A telemarketing company calls telephone numbers chosen at random. It finds that 70% of calls arc not completed (the party does not answer or refuses to talk), that 20% result in talking to a woman, and that 10% result in talking to a man. After that point, 30% of the women and 20% of the men actually buy something. What percentage of calls result in a sale? (Draw a tree diagram) What percent of sales are made to women?

We know that 70% of calls arc not completed (the party does not answer or refuses to talk), that 20% result in talking to a woman, and that 10% result in talking to a man. After that point, 30% of the women and 20% of the men actually buy something.

We calculate what percentage of calls result in a sale, and we get:

[tex]p=\frac{20}{100}\cdot \frac{30}{100}+\frac{10}{100}\cdot \frac{20}{100}\\\\p=\frac{6}{100}+\frac{2}{100}\\\\p=\frac{8}{100}[/tex]

We conclude that the 8 % of calls result in a sale.

We know that the ratio of women to men talking on the telephone is 2:1.

We calculate a percent of sales are made to women, and we get:

[tex]w=\frac{2}{3}\cdot 8\\\\w=\frac{16}{3}\\\\w=5.3[/tex]

We conclude that the 5.3% of sales are made to women.