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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.
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In a standard normal distribution what z value corresponds to 17 percent of the data between the mean and z value?
z = ±0.44
What is the z value such that 50 percent of the total area lies to the right of the curve in a normal distribution?
The Z value is 0.
Can a z score be a negative value?
Yes. However, because the distribution is symmetric about 0, some tables give only positive values for z.
What proportion of a normal distribution is located between the two z scores -1.25 and 1.25?
Approx 78.88 % Normal distribution tables give the area under the normal curve between the mean where z = 0 and the given number of standard deviations (z value) to its right; negative z values are to the left of the mean. Looking up z = 1.25 gives 0.3944 (using 4 figure tables). → area between -1.25 and 1.25 is 0.3944 + 0.3944 = 0.7888 → the proportion of the normal distribution between z = -1.25 and z = 1.25 is (approx) 78.88 %
For a normal distribution with mean -9 and standard deviation 2 The value -10 has a Z value of What?
z=(x-mu)/s = (-10+9)/2 z = -1/2 Note that the standard normal has a mean of 0, therefore: The value of -10 is to the left of the mean of -9 The value of -1/2 is to the left of the mean of 0.
