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Why are standard z values so important?

Updated: 11/4/2022
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MsumaggieL09

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14y ago

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A z-score gives the distance (specifically number of standard deviations) from the mean so when you compare z-scores, it gives a direct comparison of how far from the mean the values are.

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Q: Why are standard z values so important?
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What is the z-values associated with the middle 44 percent of the standard normal distribution?

-0.772 < Z < 0.772


How do you find a z-score?

Z Score is (x-mu)/sigma. The Z-Score allows you to go to a standard normal distribution chart and to determine probabilities or numerical values.


What does a z-score of -1.5 mean?

z-score of a value=(that value minus the mean)/(standard deviation). So a z-score of -1.5 means that a value is 1.5 standard deviations below the mean.


Is the standard normal curve is between Z -3.00 and Z 3.00?

Your question is confusing. However, I will answer the following question, and if this is not your question, please re-submit What is the area under the standard normal curve for z = -3 to Z = 3? The standard normal has a mean of zero and standard deviation of 1. The answer is: 0.9973 This is the equivalent of saying the probability of Z in the range of -3 to +3 is 0.9973 and above 3 it is 0.0027/2 or 0.00135 and below -3 it is 0.00135. Values of the normal distribution can be found in the Internet and textbooks on statistics.


How do you find the number z such that 93 percent of all observations from a standard Normal distribution are greater than z?

The tables for Z-scores are given in the form of P = Prob(Z < z) for various value of P and z. Since Prob(Z > z) = 0.93 > 0.5, then by symmetry, z < 0. So suppose z = -a where a > 0 Now Prob(Z > -a) = 0.93 is the same as Prob(Z < a) = 0.93 [because the standard Normal is symmetric]. therefore, from the tables, a = 1.4758 (approx) and so z = -1.4758 (approx).

Related questions

What percent of the Z value are positive?

The standard Normal distribution is symmetric about 0 and so 50% of the Z values are positive.


What is the z-values associated with the middle 44 percent of the standard normal distribution?

-0.772 < Z < 0.772


What is z-chart in statistics?

A z-chart in statistics is a chart that contains the values that represent the areas under the standard normal curve for the values between 0 and the relative Z-score.


What is the distribution of absolute values of a random normal variable?

It is the so-called "half-normal distribution." Specifically, let X be a standard normal variate with cumulative distribution function F(z). Then its cumulative distribution function G(z) is given by Prob(|X| < z) = Prob(-z < X < z) = Prob(X < z) - Prob(X < -z) = F(z) - F(-z). Its probability distribution function g(z), z >= 0, therefore equals g(z) = Derivative of (F(z) - F(-z)) = f(z) + f(-z) {by the Chain Rule} = 2f(z) because of the symmetry of f with respect to zero. In other words, the probability distribution function is zero for negative values (they cannot be absolute values of anything) and otherwise is exactly twice the distribution of the standard normal.


How do you find a z-score?

Z Score is (x-mu)/sigma. The Z-Score allows you to go to a standard normal distribution chart and to determine probabilities or numerical values.


Why is Z so important to the Charlie the Unicorn community?

Why is Z so important you may ask? Well its simple... Z IS FREEKIN AWSOME


Can a z score be a negative value?

Yes. However, because the distribution is symmetric about 0, some tables give only positive values for z.


How can we assess differences in quality or performance by simply comparing z values under a standard normal curve?

z value looks at standard deviations away from the mean. if its tests scores, a higher positive z value means they are higher away from the mean in a positive direction the opposite is true for a negative z score.


What does a z-score of -1.5 mean?

z-score of a value=(that value minus the mean)/(standard deviation). So a z-score of -1.5 means that a value is 1.5 standard deviations below the mean.


Is the standard normal curve is between Z -3.00 and Z 3.00?

Your question is confusing. However, I will answer the following question, and if this is not your question, please re-submit What is the area under the standard normal curve for z = -3 to Z = 3? The standard normal has a mean of zero and standard deviation of 1. The answer is: 0.9973 This is the equivalent of saying the probability of Z in the range of -3 to +3 is 0.9973 and above 3 it is 0.0027/2 or 0.00135 and below -3 it is 0.00135. Values of the normal distribution can be found in the Internet and textbooks on statistics.


What is the area between z equals 0 and z equals 2.24?

The question does not specify what z is but this answer will assume that it is the value of a random variable with a Standard Normal distribution. That being the case, the area under the curve between those values is 0.4875.


How do you find the number z such that 93 percent of all observations from a standard Normal distribution are greater than z?

The tables for Z-scores are given in the form of P = Prob(Z < z) for various value of P and z. Since Prob(Z > z) = 0.93 > 0.5, then by symmetry, z < 0. So suppose z = -a where a > 0 Now Prob(Z > -a) = 0.93 is the same as Prob(Z < a) = 0.93 [because the standard Normal is symmetric]. therefore, from the tables, a = 1.4758 (approx) and so z = -1.4758 (approx).