0
How do you compute probabilities of a standard normal random variable?
Wiki User
∙ 14y ago
You need to determine the area under the curve between the values in question. This is easy to do because there are tables that give the area values.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
What is a z score and what its used for?
The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities. However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference. The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.
What are the advantages of using the standard normal distribution over the normal distribution?
There is no simple formula to calculate probabilities for the normal distribution. Those for the standard normal have been calculated by numerical methods and then tabulated. As a result, probabilities for the standard normal can be looked up easily.
What is z value?
If a random variable (RV) X is distributed Normally with mean m and standard deviation sthenZ = (X - m)/s is the corresponding Normal variable which is distributed with mean 0 and variance 1. The distribution of X is difficult to compute but that for Z is readily available. It can be used to find the probabilities of the RV lying in different domains and thereby for testing hypotheses.
Why does a researcher want to go from a normal distribution to a standard normal distributio?
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
What is a z score and what its used for?
The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities. However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference. The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.
What is z value?
If a random variable (RV) X is distributed Normally with mean m and standard deviation sthenZ = (X - m)/s is the corresponding Normal variable which is distributed with mean 0 and variance 1. The distribution of X is difficult to compute but that for Z is readily available. It can be used to find the probabilities of the RV lying in different domains and thereby for testing hypotheses.
What are the advantages of using the standard normal distribution over the normal distribution?
There is no simple formula to calculate probabilities for the normal distribution. Those for the standard normal have been calculated by numerical methods and then tabulated. As a result, probabilities for the standard normal can be looked up easily.
What is the z value for a normal distribution?
If a random variable X has a Normal distribution with mean m and standard deviation s, then z = (X - m)/s has a Standard Normal distribution. That is, Z has a Normal distribution with mean 0 and standard deviation 1. Probabilities for a general Normal distribution are extremely difficult to obtain but values for the Standard Normal have been calculated numerically and are widely tabulated. The z-transformation is, therefore, used to evaluate probabilities for Normally distributed random variables.
Why does a researcher want to go from a normal distribution to a standard normal distributio?
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
What is z value in statistics?
A z-value is usually the result of a translation from a normally-distributed variable. Through the translation into a standard normal variable (with a mean of zero and a variance/standard deviation of one), the tables available in all statistical texts and all over the interweb can be used to calculate probabilities using the so-called "z-tables", or the fractiles of the standard normal distribution.
What is the z score for 96 percent?
1.75 using table for standard normal cumulative probabilities
What are the two parameters that are necessary to determine probabilities for a particular normal distribution curve?
Mean and Standard Deviation
What is the probability that a standard normal variable z is positive is?
It is 0.5
What role do z-scores play in the transformation of data from multiple distributions to the standard normal distribution?
None.z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.
What is the formula to convert normal distribution to the standard normal distribution?
If a variable X, is distributed Normally with mean m and standard deviation s thenZ = (X - m)/s has a standard normal distribution.
