Normal Distribution question

A consumer agency suspects that a cereal company is under¯lling packages for one of its brands. The package label states `750 grams net weight'. Experience has shown that the package weights are normally distributed with a standard deviation of 5.2 g. A random

sample of 15 packages yields a mean weight of 747 g.

(a)

Is there suffcient evidence to indicate that the true mean weight is lower than advertised? Support your answer with an appropriate hypothesis test and state yourconclusions clearly.

i know that the answers is that the true mean weight is less than advertised, but no-one has explain it to me properly can some one help???

(b)

Sketch the distributions of weights and average weights (based on 15 packages) on the same graph. Shade or indicate the area represented by the p-value.

How can i do this without actual sample weights???

Sorry if these question seem really simple, but i feel like i am getting the asnwers thrown at me with out a simple explanantion.