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It is 0.5

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Q: What is the probability that a standard normal variable z is positive is?
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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


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


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


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.


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


What is Normal of Standard Normal Probability Distribution?

with mean of and standard deviation of 1.


What are the characteristics a standard normal probability distribution?

I apologize my question should have read what are the characteristics of a standard normal probability distribution? Thank you


What is Normal of probability distribution?

with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.


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.