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What else can I help you with?
Is the normal probability distribution applied to a continuous random variable?
Yes.
Why does a researcher want to go from a normal distribution to a standard normal distribution?
A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
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.
What is the probability that a standard normal variable z is positive is?
It is 0.5
What is the probability that z (the standard normal distribution variable) is greater than 1?
It is 0.1587
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 x is within one standard deviation of its mean?
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This means that if x is a random variable that follows a normal distribution, there is about a 68% probability that x will be within one standard deviation of its mean. For distributions that are not normal, the probability may vary and would need to be determined based on the specific characteristics of that distribution.
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 P(0 z 2.53)?
P(0 < z < 2.53) refers to the probability that a standard normal random variable (z) falls between 0 and 2.53. To find this probability, you would typically look up the z-scores in a standard normal distribution table or use a calculator. The cumulative probability for z = 2.53 is approximately 0.994, and for z = 0, it is 0.5. Therefore, P(0 < z < 2.53) is approximately 0.994 - 0.5 = 0.494.
It's true or false that probability of standard normal random variable z is between 1.5 to 2.1 and is the same as the probability z is between -2.1 to -1.5?
True. Due to the symmetry of the normal distribution.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
For some positive value of Z the probability that a standard normal variable is between 0 and Z is 0.3340. the value of Z is?
0.97
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
What is the probability that the value of a randomly selected variable from a normal distribution will be more than 3 standard deviation from its mean value?
Approx 0.0027
For some positive value of x the probability that a standard normal variable is between 0 and plus 1.5x is 0.4332 what is the value of x?
1
