A bottling company wants to set its filling equipment so tha

A bottling company wants to set its filling equipment so that on the average only 3 bottles in 200 will contain less than a minimum net fill of 350 millilitres. Assuming that the fills are normally distributed with a standard deviation of 4.61 millilitres, what must be the mean fill in order to meet this requirement?

Solution

number of bottles that contain less than 3 bottles

in terms of percentage=3/200*100 =1.5%

to calculate the mean that lies between 100-1.5% =98.5% of the interval

z score corresonding to 98.5% is 2.43

2.43=350-mean/standard deviation

2.43=(350-x)/4.61

x=338.8 millilitre---->mean