SOLUTION: A quiz consists of 15 multiple choice questions. Each question has 5 choices, with exactly one correct choice. A student, totally unprepared for the quiz, guesses on each of the 15
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Question 764365: A quiz consists of 15 multiple choice questions. Each question has 5 choices, with exactly one correct choice. A student, totally unprepared for the quiz, guesses on each of the 15 questions.
a. How many questions should the student expect to answer correctly?
b. What is the standard deviation of the number of questions answered correctly?
c. If at least 9 questions must be answered correctly to pass the quiz, what is the chance the student passes?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
a. 
b. })
c. You need the probability that the student will score exactly 9 plus the probability of exactly 10 plus the probability of exactly 11, and so on all the way up to 15.
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where 
is the number of combinations of things taken at a time and is calculated by !})
You need to calculate:
\ =\ \sum_{i=9}^{15}\,{{15}\choose{i}}\left(0.2\right)^i\left(0.8\right)^{n\,-\,i})
You can do your own arithmetic. My Kentucky Windage estimate: Mighty slim \ >\ \ )
none.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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