Consider this scenario: A cereal-packing company where the content of cereal boxes must have a mean of 368 grams to satisfy the labeling on the box. Because it is expensive to weigh every box produced at the factory, a sample of boxes is used to estimate the actual mean. After analyzing the data sample, the operations manager must decide whether or not the manufacturing process is working as expected. Suppose a sample of 100 boxes is taken from thousands produced during an 8-hour shift and the standard deviation (σ) of the cereal-filling process is 12, what is the standard error of the mean? Use the equation, σX̅ = σ /(square-root of n), where n is the sample size. Enter your result as a value with one digit after the decimal point (e.g. 1.7).
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.
Question 19
Consider this scenario: A cereal-packing company where the content of cereal boxes must have a mean of 368 grams to satisfy the labeling on the box. Because it is expensive to weigh every box produced at the factory, a sample of boxes is used to estimate the actual mean. After analyzing the data sample, the operations manager must decide whether or not the manufacturing process is working as expected.
Suppose a sample of 100 boxes is taken from thousands produced during an 8-hour shift and the standard deviation (σ) of the cereal-filling process is 12, what is the standard error of the mean? Use the equation, σX̅ = σ /(square-root of n), where n is the sample size. Enter your result as a value with one digit after the decimal point (e.g. 1.7).
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