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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
What is the probability that z (the standard normal distribution variable) is greater than 1?
It is 0.1587
True or False the probability that a standard normal random variable Z is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.?
It is true because the distribution is symmetrical about Z=0.
How is probability related to the area under the normal curve?
The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.
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 the probability that a standard normal variable z is positive is?
It is 0.5
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.
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 the probability that z (the standard normal distribution variable) is greater than 1?
It is 0.1587
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
True or False the probability that a standard normal random variable Z is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.?
It is true because the distribution is symmetrical about Z=0.
How is probability related to the area under the normal curve?
The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.
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 is Normal of probability distribution?
with mean and standard deviation . Once standardized, , the test statistic follows Standard Normal Probability Distribution.
