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Answer:
0.6892 = 68.92% of bottles are within specification.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions 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.
On average, each bottle contains 2.07 liters of soda, with a standard deviation of 0.06 liters.
This means that
The plant’s quality manager wants to determine how well the process is operating.
To do this, we find the proportion of bottles within specification.
The specification limits for a bottle of soda are 2.1 liters and 1.9 liters
This is the pvalue of Z when X = 2.1 subtracted by the pvalue of Z when X = 1.9. So
X = 2.1
has a pvalue of 0.6915.
X = 1.9
has a pvalue of 0.0023
0.6915 - 0.0023 = 0.6892
0.6892 = 68.92% of bottles are within specification.