In a certain beverage manufacturer's factory, an automated soft-drink filling machine is to fill 2-litre bottles with product, the amount of soft-drink slightly varying from one 2-litre bottle to the next in according with a Normal probability model with a mean of =1.89=1.89 litres and a standard deviation of =0.05=0.05 litres.

You are to randomly pick a 2-litre bottle off the production line and measure its contents. Compute the probability that the amount of soft-drink dispensed into this bottle is between 1.83 and 1.91 litres.

Find the 90th-percentile and interpret is meaning in the context of these data.

What proportion of all 2-litre bottles will be filled to overflow?

You are to randomly pick 50 2-litre bottles for inspection, measuring the amount of product dispensed into each of the bottles. Compute the probability that between 5 and 10 of these bottles will have less than 1.85 litres of soft-drink.