Acappuccino 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

5.18oz.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Overflow only 2% of the time?

Value of when Z has a pvalue of 1-0.02 = 0.98. So X when Z = 2.055.

So the correct answer is:

5.18oz.

21

jk it's 20

step-by-step explanation: