A bottling company uses a filling machine to fill plastic bottles with a popular

Question

A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 mL. The machine is set to fill up 302 mL into a bottle.   In fact, the contents vary according to a normal distribution with a mean of 302 mL and a standard deviation = 2 mL.

a)What percentage of bottles filled by this machine are underfilled?

b)Suppose the law requires that no more than 5% of the bottles should have contents below the advertised volume (300 mL). If the standard deviation remains at 2 mL, what should be the value of the mean setting of the filling machine so that 95% of the bottles contain more than 300 mL of cola?

Explanation / Answer

Ans:

a)Bottles will be underfilled when filled quantity is less than 300

z(300)=(300-302)/2=-1

P(x<300)=P(z<-1)=0.1587

So,15.87% of the bottles are underfilled.

b)

P(Z<=z)=0.05 or P(Z>=z)=0.95

z=-1.645

-1.645=(300-mean)/2

mean=300+1.645*2=303.29

So,mean should be set to 303.29

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