Coffee in machine statistics question?
August 7th, 2011
2. The actual amount of instant coffee that a filling machine puts into 4-ounce jars may be looked upon
as a random variable having a normal distribution with σ =0.04 ounce.
a). If only 2% of the jars are to contain less than 4 ounces, what is the mean fill of these jars?
b). If the variability of the filling machine is reduced to 0.025 ounce, verify that this will lower the
required average amount of coffee to 4.05 ounces and yet keep 98% of the jars above 4 ounces.
Posted in Coffee Machine | 
Tags: filling machine, instant coffee, normal distribution, ounce jars, random variable, variability
a) From z tables , we find that a z value of 2.055 will ensure that only 2% of the jars contain less than 4 ounces, thus the mean fill of these jars = 4 + 2.055*0.04 = 4 + 0.0822 = 4.0822 = 4.08 ounces (say)
b) If the variability is reduced to 0.025 ounces, the mean fill will be
4 + 2.055*0.025 = 4 + 0.05 = 4.05 ounces