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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.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
How do you find a z score?
If you have a variable X that is normally distributed with mean m and variance s2 then the z-score, Z = (X - m)/s.Z has a standard Normal distribution.
What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
He area under the standard normal curve is?
The area under the standard normal curve is 1.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
How do you determine if the critical z value of a standard normal distribution is positive or negative?
Use the context: if the variable should be greater than the mean then z is positive and if less than the mean, it should be negative.
What is the probability that a standard normal variable z is positive is?
It is 0.5
Can the standard normal variate in normal distributions be negative?
About half the time.
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.
What is standarizing variable?
An ordinary variable is standardised by taking a linear transformation of it such that the new variable has standard properties. For example, if X is a Gaussian (Normal) variable with mean mu and standard deviation sigma, then Z = (X - mu)/sigma has a Normal distribution with mean 0 and SD = 1: it has been standardised.
What is the probability that a standard normal variable will be between the values of -2 and 1?
0.636 approx.
What is the probability that z (the standard normal distribution variable) is greater than 1?
It is 0.1587
Are all variables that are approximentaly normally distributed be transformed to standard normal variables?
Yes, to approximately standard normal.If the random variable X is approximately normal with mean m and standard deviation s, then(X - m)/sis approximately standard normal.
What is a z-score used for?
The z-score is used to convert a variable with a Gaussian [Normal] distribution with mean m and standard error s to a variable with a standard normal distribution. Since the latter is tabulated, the probability of an outcome as extreme or more compared to the one observed is easily obtained.
Given that Z is a standard normal random variable What is the value of Z if the area to the right of Z is 0.1401?
It is 1.17
