Separate individual observations from a normal sample mean

The weight of Horlicks in glass jars labelled 500 g is normally distributed with mean 505.1 g and standard deviation 7.5 g. The weight of an empty glass jar is normally distributed with mean 350 g and standard deviation 5.5 g. A glass jar’s weight is independent of the weight of Horlicks it contains.

(i) Find the probability that a randomly selected jar weighs less than 365 g and contains less than 499 g of Horlicks.

(ii) A random sample of 50 jars of Horlicks is taken and the mean Horlicks weight is calculated. (i) Find the probability that this sample mean lies between 505 g and 508 g. (ii) For 100 such samples, each of 50 jars, how many would you expect to have sample mean greater than 504 g?