The results from a statistics class’ first test are as follows: The average grade obtained on the test by its 45 students is an 85, with a standard deviation of 15 points. Answer the following based on this information: a. Approximately how many people received a failing grade (less than 65) b. What percentage of people received a grade between a 70 and a 91? c. What percentage of individuals received a score whose z-score was -.70 or less?
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.
The results from a statistics class’ first test are as follows: The average grade obtained on the test by its 45 students is an 85, with a standard deviation of 15 points. Answer the following based on this information:
a. Approximately how many people received a failing grade (less than 65)
b. What percentage of people received a grade between a 70 and a 91?
c. What percentage of individuals received a score whose z-score was -.70 or less?
d. What grade is required in order to be in the top 15 percent? The top 10 percent?
e. What percentage of people received a grade between 85 and 95?
f. What percentage of people received a grade of 94 or less?
g. What grade is required to be in the bottom 20%?
h. What z-score is required to be in the top 40%?
i. What percentage of individuals have a z-score between -1 and 1.40?
j. What percentage of individuals have a z-score between 1.05 and 1.40?
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