When we convert x-value to z- score and use Standard Normal distribution, which of the following statements is true?
a) The mean of z-score is zero and standard deviation of the z-scores is the same as
the standard deviation of original data
b) The mean and standard deviation of the z-scores is the same as the mean and standard deviation of original data
c) The mean of the z-scores is 0 and the standard deviation of z-scores is 1
d) The mean and the standard deviation of z-scores will be both zero
c) The mean of the z-scores is 0 and the standard deviation of z-scores is 1
To find the z-score for a given x-value using the standard normal distribution, you can use the formula:
z = (x - mean) / standard deviation
Now, let's analyze each statement to determine which one is true:
a) The mean of z-scores is zero and the standard deviation of the z-scores is the same as the standard deviation of the original data.
This statement is incorrect. The mean of the z-scores is indeed zero, but the standard deviation of the z-scores will be one, not the same as the standard deviation of the original data.
b) The mean and standard deviation of the z-scores is the same as the mean and standard deviation of the original data.
This statement is also incorrect. While the mean of the z-scores is the same as the mean of the original data, the standard deviation of the z-scores will not be the same as the standard deviation of the original data.
c) The mean of the z-scores is 0, and the standard deviation of the z-scores is 1.
This statement is correct. When converting a data value to a z-score using the standard normal distribution, the resulting z-scores will have a mean of 0 and a standard deviation of 1.
d) The mean and the standard deviation of the z-scores will be both zero.
This statement is incorrect. The mean of the z-scores will be zero, but the standard deviation of the z-scores will be one, not zero.
Therefore, the correct statement is:
c) The mean of the z-scores is 0, and the standard deviation of the z-scores is 1.