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30 May, 01:35

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?

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  1. 30 May, 04:07
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    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
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