written 4.3 years ago by
teamques10
★ 26k

•
modified 4.1 years ago

$\bar{X}$ = $\frac{∑(f_i x_i)}{N}$ = $\frac{(0+18+56+36+28+30+24)}{80}$ = $\frac{192}{80}$ = 2.4
$
p = \frac{\bar{X}}{n} = \frac{2.4}{6} = 0.4
$
∴ q = 1p = 10.4 = 0.6
The Binomial distribution is p(X=x) = $^nC_x p^x q^{nx}$ = $^6C_x (0.4)^x (0.6)^{6x}$
i.e. Expected frequency = $N P(X=x)$ = $80 . 6C_x(0.4)^x (0.6)^{6x}$
$$
\begin{array}{ccccccc}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
f & 4 & 15 & 25 & 22 & 11 & 3 & 0 \\ \hline
\end{array}
$$