The engineer of large manufacturing company takes many measurements of a specific dimension of components from the production line. She finds that the distribution of dimensions is approximately normal, with a mean of 3.33 cm and a coefficient of variation of 3.60%. i. What percentage of measurements will be less than 3.50 cm? ii. What percentage of dimensions will be between 3.10 cm and 3.50 cm? iii. What percentage of measurements will be equal to 3.50 cm? iv. What value of the dimension will be exceeded by 90% of the components?
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.
The engineer of large manufacturing company takes many measurements of a specific
dimension of components from the production line. She finds that the distribution of
dimensions is approximately normal, with a mean of 3.33 cm and a coefficient of variation
of 3.60%.
i. What percentage of measurements will be less than 3.50 cm?
ii. What percentage of dimensions will be between 3.10 cm and 3.50 cm?
iii. What percentage of measurements will be equal to 3.50 cm?
iv. What value of the dimension will be exceeded by 90% of the components?
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