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A test has 8 true/false questions. At least 5 questions must be answered correctly to pass the test. If a student guesses on each question, what is the probability that the student will pass the test? Round answer to three decimal places.

Solution P = 12 =05 2 = 1 = 05 n = g Binomial probability distribution P ( ac ) = n Coc p x q1-20 = 8 ( 0.5) ( 0.5) = 8. ( 0.5)8 Probability that the student will pass the test . = PC a Student must answer at least 5 quartions Correctly ) = P( 5) + P(6) + P(7) + P(8) 8 = 8 ( 0 . 5 ) + 8 ( 0.5)' + 8 ( 05 ) + 8 ( 0 5 ) 5 6 8 = 0 . 21875 + 0. 10 938 + 0. 0313 + 0.00391 = 0 . 363 34 = 0.363 (to 3 d. p)