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Are All Z Score Tables The Same

author
Maria Johnson
• Thursday, 06 May, 2021
• 8 min read

Use the negative Score table below to find values on the left of the mean as can be seen in the graph alongside. Corresponding values which are less than the mean are marked with a negative score in the z -table and represent the area under the bell curve to the left of z.

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Contents

Use the positive Score table below to find values on the right of the mean as can be seen in the graph alongside. Corresponding values which are greater than the mean are marked with a positive score in the z -table and represent the area under the bell curve to the left of z.

Q: 300 college student’s exam scores are tallied at the end of the semester. The average score for the batch was 700 (µ) and the standard deviation was 180 ().

Using the above data we need to first standardize his score and use the respective z -table before we determine how well he performed compared to his batch mates. Now that we have Eric’s Score which we know is a positive 0.56, and we know which corresponding table to pick for it, we will make use of the positive Z -table (Table 1.2) to predict how good or bad Eric performed compared to his batch mates.

(Note that this method of mapping the Score value is same for both the positive and the negative Z Scores. That is because for a standard normal distribution table, both halves of the curves on the other side of the mean are identical.

Sure it can be combined into one single larger Z -table but that can be a bit overwhelming for a lot of beginners, and it also increases the chance of human errors during calculations. If you want to know the area between the mean and a negative value you will use the first table (1.1) shown above which is the left-hand/negative Z -table.

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De Moiré came about to create the normal distribution through his scientific and math based approach to the gambling. He was trying to come up with a mathematical expression for finding the probabilities of coin flips and various inquisitive aspects of gambling.

He discovered that although data sets can have a wide range of values, we can ‘standardize’ it using a bell shaped distribution curve which makes it easier to analyze data by setting it to a mean of zero and a standard deviation of one. It was realized that normal distribution applied to many mathematical and real life phenomena.

For example, Belgian astronomer, Lambert Outlet (22nd February 1796 to 17th February 1874) discovered that despite people’s height, weight and strength presents a big range of datasets with people’s height ranging from 3 to 8 feet and with weight’s ranging from few pounds too few hundred pounds, there was a strong link between people’s height, weight and strength following a standard normal distribution curve. For example, the normal curve was used to analyze errors in astronomical observation measurements.

Whereas in probability theory a special case of the central limit theorem known as the DE Moivre-Laplace theorem states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions. This theorem appears in the second edition pf the book published in 1738 by Abraham de Moivre titled ‘Doctrine of Chances’.

They have plastic, metal, wood and even concrete picnic tables to choose from. -The Twelve Tables spelled out the Roman code of laws.

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-The Twelve Tables protected all citizens, including the plebeians. Things like the forms, reports and queries are all using data that originally comes from the tables.

Forms, queries and reports can process data to get information, like getting totals. By good programming practice, deadlocks can be avoided (but not altogether eliminated) by locking tables in the same order each time.

A Normal Standard Distribution curve is a symmetric distribution where the area under the normal curve is 1 or 100%. The standard normal distribution is a type of special normal distribution with a mean (µ) of 0 and a standard deviation of 1.

Hence, use Z Scores to transform a given standard distribution into something that is easy to calculate probabilities on. Any normal distribution with any value of mean (µ) and sigma can be transformed into the standard normal distribution, where the mean of zero and a standard deviation of 1.

A Z -scores tells how many standard deviations a value or score is from the mean (µ). This is a common transformation, so there is a reference chart that allows us to look up values.

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For example: Value of Z corresponds to an area of 0.9750 to the left of it is 1.96. A Score of 3 refers to 3 standard deviations.

Use Excel to find the actual value if your table doesn’t go that high. While the score equations look very similar, remember that calculating the standard deviation of a population is different from the way you calculate a standard deviation of a sample.

How many parts in a population will be longer or greater than some number? Example 1.1 A batch of batteries with an average of 60v and a Standard Deviation of 4v.

Answer This section requires you to be a Pass Your Six Sigma Exam member. Answer This section requires you to be a Pass Your Six Sigma Exam member.

The mean inside diameter of a sample of 200 washers produced by a machine is 0.502 inches and the standard deviation is 0.005 inches. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inches, otherwise the washers are considered defective.

(Source: www.scielo.org.mx)

Determine the percentage of defective washers produced by the machine, assuming the diameters are normally distributed. The weights of 500 American men were taken and the sample mean was found to be 194 pounds with a standard deviation of 11.2 pounds.

Question: A battery manufacturer was considering changing suppliers for a particular part. The purchasing manager required that the average cost of the part be less than or equal to $32 in order to stay within budget.

A sample of the 32 initial deliveries had a Mean of the new product upgrade price of $28 with an estimated Standard Deviation of $3. Ted Hissing I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams.

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Sources
1 www.imdb.com - https://www.imdb.com/title/tt0050079/fullcredits
2 www.fandango.com - https://www.fandango.com/the-legend-of-zorro-90900/cast-and-crew
3 www.ranker.com - https://www.ranker.com/list/full-cast-of-zorro-cast-list-for-the-show-zorro/reference
4 en.wikipedia.org - https://en.wikipedia.org/wiki/Guy_Williams_(actor)
5 en.wikipedia.org - https://en.wikipedia.org/wiki/Zorro_%281957_TV_series%29