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In a market region half of the households is known to use a particular brand of soap. In a household survey, a sample of 10 house holds are alloted to each investigator and 2048 investigators are appointed for the survey. The number of investigators likely to report that there are atleast 4 users is

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120

240

352

1696

answer is C.

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Detailed Solution

$n = 10, p = \frac{1}{2}, P (X = r) =^{10} C_{r} {(\frac{1}{2})}^{r}$

$P (X \geq 4) = 1 - P (X \leq 3) = 1 - (P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3))$

$P (X \geq 4) = 1 - (\frac{^{10} C_{0} +^{10} C_{1} +^{10} C_{2} +^{10} C_{3}}{2^{10}}) = 1 - \frac{1 + 10 + 45 + 120}{1024} = 1 - \frac{176}{1024} = \frac{848}{1024}$

The number of investigators likely to report that there are atleast 4 users is $Req. = 2048 \times P (x \geq 4), = 2048 (\frac{848}{1024}) = 1696$

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