In: Statistics and Probability
In upstate New York, milk tanker trucks follow a daily routine, stopping at the same dairy farms every day. Farm output varies due to weather, time of year, number of cows, and other factors. From years of recorded data, the mean amount of milk delivered for processing by milk tanker trucks is 7800 liters, with a standard deviation of 170 liters. Suppose 50 trucks are randomly selected. Find the probability that the mean amount of milk delivered by these trucks is more than 7760 liters. Justify your answer.