Fit a Binomial distribution to the following data

$\bar{X}$ = $\frac{∑(f_i x_i)}{N}$ = $\frac{(0+18+56+36+28+30+24)}{80}$ = $\frac{192}{80}$ = 2.4

$ p = \frac{\bar{X}}{n} = \frac{2.4}{6} = 0.4 $

∴ q = 1-p = 1-0.4 = 0.6

The Binomial distribution is p(X=x) = $^nC_x p^x q^{n-x}$ = $^6C_x (0.4)^x (0.6)^{6-x}$

i.e. Expected frequency = $N P(X=x)$ = $80 . 6C_x(0.4)^x …