A cappuccino vending machine is designed to dispense an average of? oz per cup. if the ounces per fill are normally distributed, with a standard deviation of 0.4 oz, what value should? be set at so 6 oz cups will overflow only 2% of the time? 6.82 oz 5.18 oz 5.60 oz 6.00 oz

Question

Mathematics

Lyric Pearson

29 April, 03:05

A cappuccino vending machine is designed to dispense an average of? oz per cup. if the ounces per fill are normally distributed, with a standard deviation of 0.4 oz, what value should? be set at so 6 oz cups will overflow only 2% of the time? 6.82 oz 5.18 oz 5.60 oz 6.00 oz

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Braveheart · Answer 1

Overflow 2% of the time means that the upper tail has an area of 2%, or the lower tail has an area of 100-2=98%.

From tables, P (X Z=2.0537

We want the maximum fill be 6 oz 98% of the time, or

Mean+Z * (standard deviation) = 6 oz

mean = 6oz - 2.0537*0.4=5.18 oz