Eight randomly selected batches of a chemical were tested for impurity concentration. The percentage impurity levels found in this sample were as follows: 3.2 4.3 2.1 2.8 3.2 3.6 4.0 3.8 a. Find the most efficient estimates of the population mean and variance. b. Estimate the proportion of batches with impurity levels greater than 3.75%.
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.
Eight randomly selected batches of a chemical were tested for impurity concentration. The percentage impurity levels found in this sample were as follows:
3.2 4.3 2.1 2.8 3.2 3.6 4.0 3.8
a. Find the most efficient estimates of the population
b. Estimate the proportion of batches with impurity levels greater than 3.75%.
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