SOLUTION: A math student guesses all the answers on a 15 question quiz. Assuming that the student guesses correctly 57% on each item, what is the probability of getting at most 8 answers

Hi

Note: The probability of x successes in n trials is: 

P = nCx*  where p and q are the probabilities of success and failure respectively. 

In this case p = .57 and q =.43

nCx = 

P(getting at most 8 answers correct out of 15 questions)

  1 - P(9) - P(10) - P(11) - P(12) - P(13) - p(14) - P(15) = .4847

 P(9) = 5005(.57)^9(.43)^6 for example would be P( 9 out of 15 correct)

  P(9) = 5005(.57)^9(.43)^6 = .20095

 1 - .20095 - - - - etc = .4847



Note: one may using a Binomial Distribution Calculator P(x ≤ 8)