e dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200 is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability." Suppose that scores on this test have a mean of 106 and a standard deviation of 23 . Complete the following statements about the distribution of scores on this personality test. (a) According to Chebyshev's theorem, at least ?%of the scores lie between 60 and 152 (b) According to Chebyshev's theorem, at least 36% of the scores lie between
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.
There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200 is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability."
Suppose that scores on this test have a mean of 106 and a standard deviation of 23
. Complete the following statements about the distribution of scores on this personality test.
|
(a) According to Chebyshev's theorem, at least ?%of the scores lie between 60 and 152 (b) According to Chebyshev's theorem, at least 36% of the scores lie between ? and ? (Round your answer to the nearest whole number.) |
The Chebyshev's theorem can be applied to any type of distribution. Chebyshev's theorem states that the proportion of a sample data lie between k standard deviation of the mean is,
Here,
K = positive number ≥1
This theorem states that,
1. At least 75% of all the data values should fall within 2 standard deviations of the mean.
2. At least 89%, of all data values, fall within 3 standard deviations of the mean.
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