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An example of how to calculate the passing score for a 100-question true/false test using the normal distribution, with the goal of ensuring that only 5% of students can pass by random guessing. How to apply the central limit theorem to find the mean and standard deviation of the sum of draws from a binomial distribution, and how to use normal tables to find the 95th percentile of the normal distribution, which represents the passing score.

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Pre 2010

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Download Determining Passing Score for 100-Question True/False Test with Normal Distribution and more Study notes Statistics in PDF only on Docsity! STAT 2 Lecture 22: The normal distribution for sums Today
e Example: a true/false test
e The midterm, reviewed
Example โ Each question is like a draw from the box [ 0 1 ] โ Box average = box SD = 0.5 โ Score is the sum of 100 draws with replacement from this box โ What will the probability histogram of the score look like? Example โ By the Central Limit Theorem, the sum of 100 draws from the box will be approximately normal โ Mean of normal = expected value of sum = 100*0.5 = 50 โ SD of normal = standard error of sum = sqrt(100)*0.5 = 5 Example โ Want x such that the probability of the score being greater than x is 5% โ Want the 95th percentile of the normal distribution