Auto pistons at a plant in United States are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean (mm) Range (mm) 1 2 3 4 5 156.9 153.2 153.6 155.5 156.6 4.2 4.6 4.1 5.0 4.5 a) Draw Mean chart, considering that standard deviation is 1.75. b) Draw the Mean-chart for this dimension, using the data observed in the table above. Please provide step-by-step solution
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.
Auto pistons at a plant in United States are produced in a forging process, and the diameter is a critical factor that must be controlled. From
|
Day |
Mean (mm) |
Range (mm) |
|
1 2 3 4 5 |
156.9 153.2 153.6 155.5 156.6 |
4.2 4.6 4.1 5.0 4.5 |
-
a) Draw Mean chart, considering that standard deviation is 1.75.
-
b) Draw the Mean-chart for this dimension, using the data observed in the table above.
Please provide step-by-step solution
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