Question

For the number of heads when 18 coins are tossed, find the following. Round your answers to three decimal places. Part 1 out of 2 Find the mean. Variance, and Standard deviation

Answer 1

Solution :

$\mathrm{n=18,\quad\:p=\frac{1}{2}\:\:and\:\:q=(1-p)=\frac{1}{2}.}$

$\mathrm{Mean\:\:(\mu )\:=\:n*p\:=\:18*\left ( \frac{1}{2} \right )\:=\:9}$

$\mathrm{Variance\:\:(\sigma ^{2} )\:=\:n*p*q\:=\:n*p*(1-p)\:=\:18*\left ( \frac{1}{2} \right )*\left ( 1-\frac{1}{2} \right )\:=\:18*\frac{1}{2}*\frac{1}{2}\:=\:\frac{18}{4}\:=\:\frac{9}{2}\:=\:4.5}$

$\mathrm{Standard\:deviation\:\:(\sigma )\:=\:\sqrt{\sigma ^{2}}=\:\sqrt{4.5}\:=\:2.12132\approx 2.121}$