STANDARDIZED values ( Z SCORES)

The normal distribution may be offered to calculation percentages for zones that do not enhance whole number typical deviations. To perform this, define the ar of attention by traditional deviations or fountain of a traditional deviation. Transform the actual measurement scale (in millimeters) come a standard scale ( Z ). Standardized worths ( Z ) make the typical distribution valuable for any kind of distribution that is comparable in shape to the normal curve. The devices of measure (inches, millimeters, seconds, pounds , grams, volts , ohms, etc.) will certainly not affect the calculations when the measurement range is standardized. The standardized worth ( Z ) formula because that sample data is listed below:




You are watching: A standardized value is a value found by which of the following?

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whereby


Z

=

standardized worth

x

=

value to be standardization

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=

distribution mean

s

=

distribution standard deviation


The results of the Z formula develop a range that is same to that at the bottom of figure 5.2. The size of the Z value shows how countless standard deviations the value is indigenous the distribution mean. The authorize of the answer (positive or negative) indicates whether the worth is over or below the mean.

The standardized value ( Z ) essential to prize the item elevation question is calculated below:

conference the necessary information and also illustrate the trouble (see figure 5.5). X = worth to be standardized (e.g., largest component that will certainly not jam = 7.035 mm), Xbar = circulation mean (7.008 mm), s = distribution standard deviation (0.17 mm).

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number 5.5: circulation of the elevation items.

calculation the Z value.


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round the calculated Z worth to two (2) decimal places (1.5882353 = 1.59). This is presented in number 5.6.

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figure 5.6: The relationship of the z worth to the distribution.

use Table 5.1 to recognize the area the probability.

Table 5.1: The Area under the regular Curve

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The left-hand tower of Table 5.1 is labeled Z. The number in the shaft are the units and also tenths number of the standardized Z value. For this example, the unit is 1 and the tenths digit is 5. The suitable row is emphasize in Table 5.1.

The peak row that Table 5.1 has actually labels that include x "s. The x "s stand for the units and also tenths number of the standardization Z value.

The vertical shaft of this table represents the percentage percent digit. For this example, the hundredths digit is 9. The ideal column is emphasize in Table 5.1.

The answer is found where the horizontal row 1.5 and the vertical pillar x.x9 meet. The price is 0.559. The worths that are consisted of in the body of Table 5.1 are proportions or percentages in decimal form. These numbers may be made into whole-number percentages by multiplying by 100.

0.0559 — 100 = 5.59%

This way that around 5.59% of the parts made by station No. 9 will become jammed in station 19.


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Six Sigma and also Beyond: Statistical procedure Control, Volume IV
ISBN: 1574443135EAN: 2147483647
Year: 2003Pages: 181
Authors: D.H. Stamatis
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