A machine at Ken\'s Ketchup Corporation fills 20-ounce ketchup bottles. The mach

Question

A machine at Ken's Ketchup Corporation fills 20-ounce ketchup bottles. The machine can be adjusted to pour, on average, any amount of ketchup into these bottles. However, the machine does not pour exactly the same amount of ketchup into each bottle. It varies from bottle to bottle. It is known that the net amount of ketchup poured into each jug has a normal distribution with a standard deviation of 0.25 ounce. The quality control inspector wants to adjust the machine such that a least 99% of the bottles have more than 20 ounces of ketchup. To what average should the machine be set to fill ketchup in order to meet this requirement?

Explanation / Answer

here std deviation =0.25

and for 99% level ; z=2.3263

as we know that z score =(X-mean)/std deviation

2.3263 =(20-mean)/0.25

mean =20-0.25*2.3263=19.4184

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