Q2. A firm that manufactures and bottles apple juice has a machine that automatically
hils bottles with 16 litres of juice. (The bottle can hold up to 17 litres of juice). Over a long
time, the average amount dispensed into the bottle has been 16 litres. However, there is
variability in how much juice is put in each bottle, the distribution of these amounts has a
standard deviation of llitre. If the litre of fill per bottle can be assumed to be normally
distributed, find the probability that the machine will overflow any one bottle.

With the average being 16 that means there is a 50% chance of it being 16 or below. Up to 17 is one standard deviation, or in other words an additional 34.1%. So in other words there is a 50% + 34.1% chance of the bottle being filled to 17 liters or less. that means whatever is left represents more than 17 liters, which is what we are interested in. so 100 - 50 - 34.1 = 15.9%

When dealing with standard deviation keep in mind one standard deviation away is 34.1%, so if you go one less and one more that encompasses 68.2%, two standard deviations away is 34.1% + 13.6%, and going both ways again doubles that. Hopefully you have an image of a bell curve showing the standard deviation breakup, if not try and find one online.