The weights of chickens grown in a certain poultry farm are normally distributed with a standard deviation of 1.2 pounds. The owner of the poultry farm claims that the mean weight of this chicken in a period of three months is more than 7.6 pounds. Suppose a random sample of 100 chickens will have an average weight of 7.8 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. (5 Marks)