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3.93 Manufacturing and Product Development Paint viscosity is a measure of thickness that determines whether the paint will cover in a single coat. A random sample of latex paint viscosities (in KU, or Krebs units) was obtained, and the data are given in the following table: viscos 113 124 141 115 115 129 113 129 112 112 a. Find the mean and the standard deviation for this data. b. Find the z-score for each observation. c. Find the mean and the standard deviation for all of the z-scores. d. For any set of observations, can you predict the mean and standard deviation of the corresponding z-scores? Try to prove this result. Part (d). What exactly is the question asking to find, and how do I solve the problem? Please explain with detail as to how I can approach the problem
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Answer #1

d)

For any sample if we calculate corresponding Z-Score for each data-point and then calculate the mean and Std Deviation of all the z-scores, then always, mean will be zero and std deviation will be 1.

Eg:

Z Score 113-0.73 124 141 115-0.53 115-0.53 0.37 2.08 113-0.73 0.87 112-0.83 112-0.83 0.00 1.00 Mean Std Dev 120.3 9.97 1

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