A student takes a multiple-choice exam with 10 questions, each with four possibl
ID: 2956304 • Letter: A
Question
A student takes a multiple-choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60%, or better. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Find the probability that the studenta. get at least one question right
b. passes the exam
c. recieves an "A" on the exam (90% or better)
d. how many questions would you expect the student to get correct?
e. Obtain the standard deviation of the number of questions that the student gets correct.
Explanation / Answer
Given there are 10 questions and there are four possible selection.So probavility of right answer, p=1/4 Probability of wrong answer,1-p=1-(1/4) =3/4 -------------------------------------------------------------------------------- a) P(getting at least one question right )=P(x>=1) =1-P(0) =1-[C(10,0)*(1/4)0*(3/4)10] =1-[0.0563] =0.9436 ------------------------------------------------------------------------------- b)Given for passing he must get 60%.i.e. he must have 6 correct answers P(Passing the exam) =P(x>=6) =C(10,6)*(1/4)6*(3/4)4 +C(10,7)*(1/4)7*(3/4)3 +C(10,8)*(1/4)8*(3/4)2 +C(10,9)*(1/4)9*(3/4)1 +C(10,10)*(1/4)10*(3/4)0 = 0.0197 ------------------------------------------------------------------------------------ C)P(he receives A grade of better) =P(x>=9) =C(10,9)*(1/4)9*(3/4)1 +C(10,10)*(1/4)10*(3/4)0 =0.00002956 --------------------------------------------------------------------------------- d) Number of questions that will be correct will be the mean of the distribution =np =10*(1/4) =2.5 -------------------------------------------------------------------------------- e)standard deviation of the number of questions that the student gets correct =vnp(1-p) =v10*(1/4)*(3/4) =v1.875 =1.3693 --------------------------------------------------------------------------------- ---------------------------------------------------------------------------------
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