The amount of fill in a half-liter (500ml) soft drink bottle is normally distrib

Question

The amount of fill in a half-liter (500ml) soft drink bottle is normally distributed. The process has a standard deviation of 5.5 ml. The mean is adjustable. Where should the mean be set to ensure a95 percent probability that a half-liter bottle will not be underfilled? Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled? Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled? Find the standard normal area for each of the following

Explanation / Answer

a) =NORMSINV(0.95)=1.644854

The mean set to be ensure a 95% probability that half litre bottle will not be underfilled is

= 1.644854*5.5 + 500 = 509.05

b)1

=NORMSINV(0.99)=2.32635

The mean set to be ensure a 99% probability that half litre bottle will not be underfilled is

= 2.32635*5.5 + 500 = 512.79

c)

The mean set to be ensure a 99.9% probability that half litre bottle will not be underfilled is

= 3.0902*5.5 + 500 = 517

a) P(1.21<Z<2.11) =0.0957

b)P(2<Z<3) =0.0214

c) P(-2<Z<2) =0.9545

d)P(Z>0.5) =0.3085

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