Your first assignment at El Smello Perfume Co. is to determine the proper settin

Question

Your first assignment at El Smello Perfume Co. is to determine the proper setting for the automatic bottle filler. Each bottle states that it contains 100 mL and government regulations stipulate that no more than 2.5% of the bottles may contain less than the stated volume. Obviously, the company wants to put no more than the minimumin each bottle, but still abide by regulations.
(a)If the standard deviation in filling each bottle is 2.0 mL, what should be the setting of the bottle filler? (Assume the population exhibits a Gaussian distribution.)
(b)Prior to your adjusment, the bottle filler was set to 110.0 mL, just to be on the safe side. If El Smello produces 100,000 bottles per year at a cost of $0.20 per mL, how much money will your adjustment save the company in one year?

Explanation / Answer

a)P(X<100)=0.025

Hence Z=-1.96, Hence Mean=100+1.96*2=103.92ml

Hence mean has to be set to 96.08ml

b)money saved=(110-103.92)*100000*0.02=$12,160

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