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Stats A test consists of 15 multiple choice questions. Each question has 5 possible answers of  which only one is correct. Answers Let X be the number of correct answers guessed. Clearly X is binomial with n =15 and p =  1/5 = 0.20.  The probability mass function binomial variable is given by  ( ) (1 ) x n x x P X x nC p p - = = - .The probability for different values of x are given below. cumulative X p(X) probability 0 0.035184372088832 0.035184372088832 1 0.131941395333120 0.167125767421952 2 0.230897441832960 0.398023209254912 3 0.250138895319040 0.648162104573953 4 0.187604171489280 0.835766276063233 5 0.103182294319104 0.938948570382337 6 0.042992622632960 0.981941193015297 7 0.013819057274880 0.995760250290177 8 0.00345476431872 0 0.999215014608897 9 0.00067175972864 0 0.999886774337537 10 0.00010076395929 6 0.999987538296833 11 0.00001145044992 0 0.999998988746753 12 0.00000095420416 0 0.999999942950913 13 0.00000005505024 0 0.999999998001153 14 0.00000000196608 0 0.999999999967233 15 0.00000000003276 8 1.000000000000000 1.00000 a) What is the probability the student will guess them all right? P (the student will guess them all right) = P (X = 15)                                                           =  0.000000000032768   b) The probability that he will guess AT MOST 12 correct. P (he will guess AT MOST 12 correct) = P (X   12)

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