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In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes
is respectively given by
Options:
is respectively given by
Solution:
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Verified Answer
The correct answer is:
$\frac{8}{3}, \frac{4}{3}$
5 or 6 is success
$\therefore p=\frac{2}{6}=\frac{1}{3}$
$\therefore q=1-\frac{1}{3}=\frac{2}{3}$
$\mathrm{n}=8$
$\therefore$ Mean $=\mathrm{n} \mathrm{p}=8\left(\frac{1}{3}\right)=\frac{8}{3}$
Standard deviation $=\sqrt{n p q}=\sqrt{8\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)}$
$=\sqrt{\frac{16}{9}}=\frac{4}{3}$
$\therefore p=\frac{2}{6}=\frac{1}{3}$
$\therefore q=1-\frac{1}{3}=\frac{2}{3}$
$\mathrm{n}=8$
$\therefore$ Mean $=\mathrm{n} \mathrm{p}=8\left(\frac{1}{3}\right)=\frac{8}{3}$
Standard deviation $=\sqrt{n p q}=\sqrt{8\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)}$
$=\sqrt{\frac{16}{9}}=\frac{4}{3}$
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