14) PART A, Captain Obvious scored a 73 on his Psychology Test and a 67 on his English test. He believes he did better (relative to his classmate) on the Psychology Test than on the English test. Given that the Psychology test had a mean of 81 and a standard deviation of 5, and the English test had a mean of 77 and a standard deviation of 10. Was Captain Obvious correct? PART B, What if Captain Morgan scored a 75 on his History Test and a 60 on his Sociology test. He believes he did better (relative to his classmate) on the History Test than on the Sociology test. Given that the History test had a mean of 88 and a standard deviation of 13, and the Sociology test had a mean of 87 and a standard deviation of 9. Was Captain Morgan correct?
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.
14) PART A, Captain Obvious scored a 73 on his Psychology Test and a 67 on his English test. He believes he did better (relative to his classmate) on the Psychology Test than on the English test. Given that the Psychology test had a mean of 81 and a standard deviation of 5, and the English test had a mean of 77 and a standard deviation of 10. Was Captain Obvious correct?
PART B, What if Captain Morgan scored a 75 on his History Test and a 60 on his Sociology test. He believes he did better (relative to his classmate) on the History Test than on the Sociology test. Given that the History test had a mean of 88 and a standard deviation of 13, and the Sociology test had a mean of 87 and a standard deviation of 9. Was Captain Morgan correct?
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