For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. a)A score of X 74 on an exam with M 82 and s 8; or a score of X 40 on an exam with μ 50 and s 20. b)A score of X 51 on an exam with μ 45 and s 2; or a score of X 90 on an exam with μ 70 and s 20. c)A score of X 62 on an exam with μ 50 and s 8; or a score of X 23 on an exam with μ 20 and s 2.
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.
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For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.
a)A score of X 74 on an exam with M 82 and
s 8; or a score of X 40 on an exam with
μ 50 and s 20.
b)A score of X 51 on an exam with μ 45 and
s 2; or a score of X 90 on an exam with
μ 70 and s 20.
c)A score of X 62 on an exam with μ 50 and
s 8; or a score of X 23 on an exam with μ 20 and s 2.
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