A sample has a mean of M = 80 and a standard deviation of s = 10. For this sample, find the X value corresponding to each of the following z-scores. z = 0.80, z = 1.20, z = 2.00 z = -0.40, z = -0.60, z = -1.80
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A sample has a mean of M = 80 and a standard deviation of s = 10. For this sample, find the X value corresponding to each of the following z-scores.
z = 0.80, z = 1.20, z = 2.00
z = -0.40, z = -0.60, z = -1.80
Given:
The sample mean is M=80.
The standard deviation is s=10.
The z score is calculated as:
The value of X, when the z score is 0.80 is given as:
Therefore, the value of X is 88.
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