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31 December, 19:44

Q 2.20: In a survey, there are two categories of respondents, employed and unemployed people, and two options, A and B. The proportion of those who have chosen option B is greater than 0.5 among the total number of the respondents, but is lower than 0.5 among the unemployed respondents. We know that 314 employed and 512 unemployed people chose option A and 356 employed chose option B. How many unemployed people chose option B

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  1. 31 December, 21:42
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    The answer is 508

    Step-by-step explanation:

    Solution

    First of all, the proportion of B is exceeds 0.5 in total.

    Now,

    To find the total of A it we have A = 314 + 512 = 826

    The number of employed that choose B = 356

    For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed

    what this suggest is that the employed B is greater than 826-356 = 470

    So,

    The respondent that are unemployed that choose B must be greater than 470

    Thus,

    We recall that the B proportion among the unemployed respondent is lesser than. 50

    Thus suggests that the respondent that are unemployed who choose be is lesser than 512

    The conditions becomes

    470 lesser than the number of unemployed respondents who selected B lesser than 512

    Hence the needed number of the number of unemployed respondents who chose B should be between 470 and 512

    So, possible answer here is 508.
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