A bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (mL) and standard deviation The fill volumes are normally distributed. What proportion of bottles have volumes less than 1,007 mL?

0.5 = 50% of bottles have volumes less than 1,007 mL

Step-by-step explanation:

Problems of normally distributed samples are 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 question, we have that:

What proportion of bottles have volumes less than 1,007 mL?

This is the pvalue of Z when X = 1007. So

has a pvalue of 0.5

0.5 = 50% of bottles have volumes less than 1,007 mL

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step-by-step explanation: