Two language majors, Anna and Megan, took exams in two languages. Anna scored 82 on both exams. Megan scored 71 on the first exam and 94 on the second exam. Overall student scores on the first exam had a mean of 82 and a standard deviation of 5 and the second exam scores had a mean of 74 and a standard deviation of 14. To qualify for language honors, a major must maintain at least an 85 average across all language courses taken. So far, which of Anna and Megan qualify? Which student's overall performance was better?
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.
Two language majors, Anna and Megan, took exams in two languages. Anna scored 82 on both exams. Megan scored 71 on the first exam and 94 on the second exam. Overall student scores on the first exam had a mean of 82 and a standard deviation of 5 and the second exam scores had a mean of 74 and a standard deviation of 14. To qualify for language honors, a major must maintain at least an 85 average across all language courses taken. So far, which of Anna and Megan qualify? Which student's overall performance was better?
Given Information:
Anna scored 82 on both exams.
Megan scored 71 on the first exam and 94 on the second exam.
First Exam:
Mean
Standard deviation
Second Exam:
Mean
Standard deviation
To qualify for language Honours, a major must maintain at least an 85 average across all language courses taken:
Take the average of scores:
Anna:
Megan:
Since, their averages are less than 85, no student qualifies for language honours.
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