A manufacturer of industrial solvent guarantees its customer

A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 103.3 pounds and a standard deviation of 3.93 pounds.

What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?

Solution

A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 103.3 pounds and a standard deviation of 3.93 pounds.

What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?

Z value for upper 99% area is -2.326

Ie.      p( z > -2.326) =0.99

(100-103.3)/s = -2.326

S=3.3/2.326 =1.419

The required SD = 1.419