In a recent year, grade 6 Ohio State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36. Possible test scores could range from 0 to 1000. Assume that the scores were normally distributed. This is not a normal approximation, so do not correct for continuity. Find the probability that a student had a score higher than 295. Find the probability that a student had a score between 230 and 305. What is the highest score that would still place a student in the bottom 16% of the scores?
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.
In a recent year, grade 6 Ohio State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36. Possible test scores could
Find the probability that a student had a score higher than 295.
Find the probability that a student had a score between 230 and 305.
What is the highest score that would still place a student in the bottom 16% of the scores?
If 4000 students are randomly selected, how many will have a test score that is less than 300?
A random sample of 40 students is drawn from this population. What is the probability that the mean test score is greater than 290?
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