Question

A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements?

Answer 1

Answer:

Expected number of subscribers in the sample who read the advertisements=42

Step-by-step explanation:

Step 1

Determine the proportion of both men and women subscribers as shown;

Proportion of Men subscribers=number of men subscribers/total number of subscribers

where;

number of men subscribers=980,000

total number of subscribers=number of men+number of women

total number of subscribers=(980,000+640,000)=1,620,000

replacing;

proportion of men subscribers=980,000/1,620,000=98/162

Step 2

Proportion of women subscribers=1-(98/162)=64/162

Step 3

Expected proportion of men that read the advertisement=(50/100)×(98/162)=4,900/16,200=49/162

Expected proportion of women that read the advertisement=(30/100)×(64/162)=1,920/16,200=192/1620

Step 4

Total number of proportion=(49/162)+(192/1620)=341/810

Expected number from the sample=(341/810)×100=42

Expected number of subscribers in the sample who read the advertisements=42