Two college roommates are taking different physics courses at a university. They agree to a wager regarding their midterm scores, whereby the loser must do the dishes for a month. After scoring an 82, Jacob insists that Michael lost since he earned a 70 on his exam. However, Michael argues that he performed better relative to the rest of his class than did Jacob. Use the given class results to determine who won the bet.
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.
Exercise 1. Two college roommates are taking different physics courses at a university. They agree to a wager regarding their
midterm scores, whereby the loser must do the dishes for a month. After scoring an 82, Jacob insists that Michael lost since he
earned a 70 on his exam. However, Michael argues that he performed better relative to the rest of his class than did Jacob.
Use the given class results to determine who won the bet.
Jacob’s class: x = 78 , s = 6
Michael’s class: x = 55 , s = 12
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