I begin by stating the question: In a certain city, milk tanker trunks follow a daily routine, stopping at the same dairy farms every day. Farm output, however, varies because of weather, time of the year, number of cows, and other factors. From years of recorded data, the mean amount of milk picked up by a truck for processing is 7,750 litres, with a standard deviation of 150 litres. Suppose 36 trucks are randomly selected.

(a) Find the probability that the sample mean amount of milk picked by the 36 trucks is more than 7,800 litres.

(b) Find the value m such that the probability that the sample mean is less than m is 0.1

Here, I have trouble finding which method is the most approriated. I think I could use the standard deviation to calcate probability, yet I can't thing conclusive results.

Hence, how would you have proceed?