A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine. a) Find the mean of the total volume of the beverage in the case. b) Find the standard deviation of the total volume of the beverage in the case. c) Find the mean of the average volume per bottle of the beverage in the case. d) Find the standard deviation of the volume per bottle of the beverage in the case. e) How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A machine that fills bottles with a beverage has a fill volume whose
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