A professor decides to give a 20-question true false quiz. She wants to choose the passing grade such that?

the probability of passing a student who guesses on every question is less than .05. What score should she set as the lowest passing grade?A professor decides to give a 20-question true false quiz. She wants to choose the passing grade such that?
The odds of getting exactly n right when guessing is:





C(20,n)(1/2)^20





You want to find the smallest k such that:





sum (n=k;20) C(20,n) (1/2)^20 %26lt; 0.05





Or:





sum(n=k;20) C(20,n) %26lt; 2^20/20 = 2^18/5





The value k=14 is the first such that this sum is greater, so the smallest is k=15.





That means you can set passing grade for 75%, which has a 2.1% chance of being scored by guessing.





The odds hat you can get 70% or better by guessing is 5.8%.A professor decides to give a 20-question true false quiz. She wants to choose the passing grade such that?
14/20
16/20. Or 80 percent which is equal to 16/20