A soft drink bottling machine can be regulated so that itdischarges an average o

Question

A soft drink bottling machine can be regulated so that itdischarges an average of
ounces per cup. If the ounces of filling are normally distributedwith standard deviation
of 0.3 ounces, give the setting for so that 8-ounce cupswill overflow only 1% of the
time.

Explanation / Answer

A soft drinkbottling machine can be regulated so that it discharges an averageof ounces per cup. If the ounces of filling are normally distributedwith standard deviation of 0.3 ounces, give the setting for so that 8-ounce cups willoverflow only 1% of the time. {Required} ---->    Prob{8 oz Cup Overflows} = 0.01 ---->    Prob{Z > ((8 oz)- )/} = 0.01 ---->    Prob{Z > ((8) - )/(0.3)} = 0.01 ---->    Z = 2.326    (    ((8) -)/(0.3) = 2.326 ---->    8 - = (0.3)*(2.326) ---->    = 8 - (0.3)*(2.326) ---->    = 7.3 ounces .

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