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A vending machine i deigned to dipene a mean of oz of coffee into an​ 8-oz cup. If the tandard deviation of the amount of coffee dipened i oz and the amount i normally​ ditributed, determine the percent of time the machine will dipene more than oz



Answer :

The percent of time the machine will dispense more than oz is 59.87%

Define mean and standard deviation.

The standard deviation (SD) is a commonly used measure of variability in statistics. It displays the amount of variance from the mean (mean). A low SD implies that the data points are close to the mean, whereas a high SD suggests that the data are dispersed across a wide range of values.

Given

Mean = 7.6

Standard deviation = 0.4

Data value = 7.7

The z-score is calculated by subtracting the data value from the mean and dividing it by the standard deviation.

Z = 7.7 - 7.6/0.4

Z = 0.1/0.4

Z = 0.25

In the column beginning with.05 of the standard normal distribution table.

= 0.5987

= 59.87%

The percent of time the machine will dispense more than oz is 59.87%

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