A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 47.1, with a standard deviation of 9.9. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year. (a) According to Chebyshev's theorem, at least ? of the scores lie between 27.3 and 66.9. (b) According to Chebyshev's theorem, at least 56% of the scores lie between O and . (Round your answer to 1 decimal place.)
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.
Introduction:
Suppose X is a random variable with expectation, μ and standard deviation, σ. Then, for any positive real number k, according to Chebyshev’s Inequality, it can be said that:
P (| X – μ | < kσ) ≥ 1 – (1/k2).
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