The weights of chickens grown in a certain poultry farm are normally distributed with a standard deviation of $1\mathrm{.}2$ pounds. The owner of the poultry farm claims that the mean weight of this chicken in a period of three months is more than $7\mathrm{.}6$ pounds. Suppose a random sample of $100$ chickens will have an average weight of $7\mathrm{.}8$ pounds.

a$)$ Is this strong enough evidence to reject the claim stated by the owner at the $5\%$ level of significance?

b$)$ Also find P$-$Value.