The fill volume of an automated filling machine used for filling cans of carbona

Question

The fill volume of an automated filling machine used for filling cans of carbonated beverage is normaly dstobuted. Suppose, that the mean of che ing operation can be (a) At what value should the mean be set so that 99.9% of all cans exceed 14 fluid ounces? Round your answer to three decimal places (e. 98,765) fluid ounces (b) At what value should the mean be set so that 99 9% of all cans exceed 14 fluid ounces if the standard deviation-can be redend to 007 rild Round your answer to three decimal places (e.g. 98.765) fluid ounces

Explanation / Answer

Ans:

a)

P(Z>z)=0.999

P(Z<=z)=1-0.999=0.001

z=normsinv(0.001)=-3.090

z=(14-mean)/0.2

-3.090=(14-mean)/0.2

mean=14+3.090*0.2=14.618

b)

-3.090=(14-mean)/0.07

mean=14+3.090*0.07=14.216

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