Question

Assuming that half of the population are consumers of rice so that the chance of an individual being a consumer is $1/2$ and assuming that $1024$ investigators each take $10$ individuals to see whether they are consumers, the number of investigators you expect to report that three or less are consumers is

• A. $360$
• B. $240$
• C. $176$
• D. $60$

Answer 1

Answer: (C)

$176$

$E\{X=n\}=\left(\begin{array}{c}10\\ n\end{array}\right)\ast {\frac{1}{2}}^n\ast {\frac{1}{2}}^{10-n}\ast (no.ofinvestigator)E\{X=0\}+E\{X=1\}+E\{X=2\}+E\{X=3\}=\left(\begin{array}{c}10\\ 0\end{array}\right)\ast {\frac{1}{2}}^0\ast {\frac{1}{2}}^{10}\ast 1024+\left(\begin{array}{c}10\\ 1\end{array}\right)\ast {\frac{1}{2}}^1\ast {\frac{1}{2}}^9\ast 1024+\left(\begin{array}{c}10\\ 2\end{array}\right)\ast {\frac{1}{2}}^2\ast {\frac{1}{2}}^8\ast 1024+\left(\begin{array}{c}10\\ 3\end{array}\right)\ast {\frac{1}{2}}^3\ast {\frac{1}{2}}^7\ast 1024E\{X=0\}+E\{X=1\}+E\{X=2\}+E\{X=3\}=176$