Q: Why you use z distribution?

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You calculate the z-scores and then use published tables.

If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.

For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.

Tables of the cumulative probability distribution of the standard normal distribution (mean = 0, variance = 1) are readily available. Almost all textbooks on statistics will contain one and there are several sources on the net. For each value of z, the table gives Î¦(z) = prob(Z < z). The tables usually gives value of z in steps of 0.01 for z â‰¥ 0. For a particular value of z, the height of the probability density function is approximately 100*[Î¦(z+0.01) - Î¦(z)]. As mentioned above, the tables give figures for z â‰¥ 0. For z < 0 you simply use the symmetry of the normal distribution.

If X is Normally distributed with mean 65 seconds and sd = 0.8 seconds, then Z = (X - 65)/0.8 has a Standard Normal distribution; that is, Z has a N(0, 1) distribution. The cumulative distribution for Z is easily available - on the net and in any basiic book on statistics. To get to the cumulative dirtribution function of X all you need is to use the transformation X = 0.8*Z + 65.

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If the distribution is Gaussian (or Normal) use z-scores. If it is Student's t, then use t-scores.

If the sample size is large (>30) or the population standard deviation is known, we use the z-distribution.If the sample sie is small and the population standard deviation is unknown, we use the t-distribution

You calculate the z-scores and then use published tables.

If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.

For statistical tests based on (Student's) t-distribution you use the t-table. This is appropriate for small sample sizes - up to around 30. For larger samples (or degrees of freedom), the t-distribution becomes very close to the Standard Normal distribution so you use the z-tables.

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.

11.51% of the distribution.

Tables of the cumulative probability distribution of the standard normal distribution (mean = 0, variance = 1) are readily available. Almost all textbooks on statistics will contain one and there are several sources on the net. For each value of z, the table gives Î¦(z) = prob(Z < z). The tables usually gives value of z in steps of 0.01 for z â‰¥ 0. For a particular value of z, the height of the probability density function is approximately 100*[Î¦(z+0.01) - Î¦(z)]. As mentioned above, the tables give figures for z â‰¥ 0. For z < 0 you simply use the symmetry of the normal distribution.

If X is Normally distributed with mean 65 seconds and sd = 0.8 seconds, then Z = (X - 65)/0.8 has a Standard Normal distribution; that is, Z has a N(0, 1) distribution. The cumulative distribution for Z is easily available - on the net and in any basiic book on statistics. To get to the cumulative dirtribution function of X all you need is to use the transformation X = 0.8*Z + 65.

z- statistics is applied under two conditions: 1. when the population standard deviation is known. 2. when the sample size is large. In the absence of the parameter sigma when we use its estimate s, the distribution of z remains no longer normal but changes to t distribution. this modification depends on the degrees of freedom available for the estimation of sigma or standard deviation. hope this will help u.... mona upreti.. :)

0% of a normal (of any) distribution falls between z 1.16 and z 1.16. 1.16 - 1.16 = 0.

Z is the standard normal distribution. T is the standard normal distribution revised to reflect the results of sampling. This is the first step in targeted sales developed through distribution trends.