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 48.4 , with a standard deviation of 9.1 . 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 ?56%75%84%89% of the scores lie between 30.2 and 66.6 . (b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the scores lie between and . (Round your answer to 1 decimal place.) (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between and . (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the scores lie between 30.2 and 66.6 .
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) According to Chebyshev's theorem, at least ?56%75%84%89% of the scores lie between 30.2 and 66.6 .
(b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the scores lie between
(c) Suppose that the distribution is bell-shaped. According to the
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the scores lie between 30.2 and 66.6 .
|
|
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
