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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 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.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
What requirements are necessary for a normal probability distribution to be a standard normal probability?
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
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 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.
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 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.
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 requirements are necessary for a normal probability distribution to be a standard normal probability?
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
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
