Don't fret; its only probability

[khalil]

Weird topic name huh? Just wanted to be different.

New Question:

From essentials ch 18 Q8

The volume of soft drink in a 1 litre bottle is normally distributed. The soft drink company
needs to calibrate its filling machine. They don’t want to put too much soft drink into each
bottle, as it adds to their expense. However, they know they will be fined if more than 2%
of bottles are more than 2 millilitres under volume. The standard deviation of the volume
dispensed by the filling machine is 2.5 millilitres. What should they choose as the target
volume (i.e. the mean of the distribution)? Give your answer to the nearest millilitre.

ans: 1004 ml

[Mao]

Pr( X < 998 ) = 0.02 = Pr( Z < -2.05 ) [from InvNorm on calc]



If they set mean = 1003, this implies slightly more than 2% will be more than 2mL under volume, which incurs a fine. Hence the target volume must be set on 1004 mL

[khalil]

Thanks Mao.
Quick question: when we use the inverse function, why do we assume the the mean is 0 and s.d is 1?