The diameter of oranges from a Florida orchard are normally distributed with mean 3.2 inches and a standard deviation of 1.1 inches. A packing supplier is designing special occasion presentation boxes for oranges and needs to know the average diameter for a random sample of 8 oranges. For a random sample of 8 oranges is to be taken from this orchard what is the probability that the mean diameter of these oranges will be smaller than 3 inches? Round your answer to 4 decimal places.