This question is from Binomial distribution.

Let $X$=Distribution function which is no. of success.

$p=$ Probability of success=Probability of getting $1$ or $5=\large\frac{2}{6}=\frac{1}{3}$

$q=$ Probability of failure=$1=\large\frac{1}{3}=\frac{2}{3}$

$n=120$

$P(X=r)=^nC_r.p^r.q^{n-r}$

Mean of the distribution $=np=120\times\large\frac{1}{3}=$$40$

Variance of the distribution $=npq=120\times\large\frac{1}{3}$$\times\large\frac{2}{3}=\frac{80}{3}$