question is about normal distribution

Question

The actual amount of instant coffee that a filling machine puts in to “4”ounce jars may be looked upon as a random variable having a normal distribution with σ = 0.04 ounce. If only 2% of the jars are to contain less than 4 ounces, what should be the mean fill of these j

Answer 1

Let X be the random variable representing the amount of instant coffee in 4 oz jars, then

P{X≤4} = 0.02.  From a Standard Normal Distribution table, the corresponding z score is -2.05

 

If μ is the mean fill of the jars

z = (X-μ)/σ

 

For X = 4, z = -2.05 and σ = 0.04, the mean fill μ is 4.08 oz