Question

A machine is used to fill soda bottles in a factory. The bottles are labeled as containing 330 ml, but extra room at the top of the bottle allows for a maximum of 25ml of soda before the bottle overflows. The standard deviation of the amount of soda put into the bottles by the machine is known to be 5 ml. i)What proportion of overflow If it is set to mean 340ml? ii)what standard deviation would allow for no more than 3% of bottles to be overfilled?iii)If management require no more than 5%of bottlesshould be overfilled,so the machine should be set to fill the bottles with what mean amount?.

Answer 1

From the given information, the soda will be overflow when the bottles are filled more than 330+25=355ml

The standard deviation of the amount of soda put into the bottles by the machine is known to be 5 ml.

Let X be the amount of soda filled in a bottles.

i) The proportion of overflow If it is set to mean 340ml is given by:

ii) The standard deviation would allow for no more than 3% of bottles to be overfilled is obtained by using:

Therefore in order to allow for no more than 3% of bottles to be overfilled the standard deviation should be atleast 5.36

iii) The mean amount of bottles filled by machine set so that no more than 5% of bottlesshould be overfilled is given by:

Therefore the mean should be atleast 346.8 ml.