Determining Passing Score for 100-Question True/False Test with Normal Distribution, Study notes of Statistics

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STAT 2

Lecture 22:

The normal distribution

for sums

Today ● Example: a true/false test ● The midterm, reviewed

Example ● For each question, chance of getting it right by guessing is 50% ● Assume getting any question right is independent of getting any other question right ● The number of correct answers will have a binomial distribution; however, it's hard to use the binomial to answer this question

Example ● Each question is like a draw from the box [ 0 1 ] ● Box average = box SD = 0. ● Score is the sum of 100 draws with replacement from this box ● What will the probability histogram of the score look like?

Example ● Want x such that the probability of the score being greater than x is 5% ● Want the 95 th percentile of the normal distribution

Example ● From normal tables, 95 th percentile of the standard normal is 1. ● Change from standard normal to our normal by multiplying by SD and adding mean: 1.64*5 + 50 =

● To be safe, make 59 the passing score