The volume of coffee, VVV ml, dispensed by an automated brewing machine is normally distributed with a mean of 340 ml and a standard deviation of 15 ml. Servings containing more than 365 ml are categorized as 'Premium' servings.
Determine the proportion of servings categorized as 'Premium'.
The manufacturer wants to award a 'Standard' quality mark to the servings in the top 90%, which are those containing at least kkk ml. Find the value of kkk.
Within the 'Premium' category, the largest 15\frac{1}{5}51 of servings are further designated as 'Gold Reserve'. Find the minimum volume, sss, required for a 'Gold Reserve' designation.
A quality control officer randomly selects 5 servings that were already categorized as 'Premium'. Find the exact probability that at least one of these is a 'Gold Reserve' serving.