Credit for a philosophy class can be obtained by taking a true-false 100 questio

Question

Credit for a philosophy class can be obtained by taking a true-false 100 question exam. The questions are independent of each other which means that knowing (or not knowing) the answer to a question does not help to answer any of the remaining questions. Answering 90 or more questions correctly earns not only earns credit for the class but also an A grade is recorded. Answering at least 60 questions correctly, simply earns credit, which is recorded as CR in the transcript.

a) For a completely unprepared test taker who must guess the answer to each question (p = 0.5), what is the probability of getting credit with an A recorded? What is the probability of just earning credit? Answer these two questions for the case of a prepared test taker for whom the probability of giving a correct answer to a question is p =0.8.

Explanation / Answer

Mean = np = 100 *0.5 = 50

Standard deviation = Önpq = Ö[100*0.5*(1-0.5)] = 5

P (x>= 90) = P ( x >= 89.5)   [Using correction factor]

Z = ( x – Mean ) / Standard deviation

   = (89.5 – 50)/5

   = 7.9

P ( z > 7.9 ) = 1 – P ( z < 7.9 ) = 1 – 0 = 1

Answer: 1

P (x>= 60) = P (z>= 59.5) [Using correction factor]

z = (59.5 – 50)/5

= 1.9

P (z>1.9) = 1 – P ( z <1.9)

                = 1 – 0.9713

                              = 0.0287

              Answer : 0.0287

Mean = np = 100 *0.8 = 80

Standard deviation = Önpq = Ö[100*0.8*(1-0.8)] = 4

P (x>= 90) = P ( x >= 89.5)   [Using correction factor]

Z = ( x – Mean ) / Standard deviation

   = (89.5 – 80)/4

   = 2.38

P ( z > 2.38 ) = 1 – P ( z < 2.38 ) = 1 – 0.9913 = 0.0087

Answer: 0.0087

P (x>= 60) = P (z>= 59.5) [Using correction factor]

z = (59.5 – 80)/4

= -5.13

P (z>-5.13) = 1 – P ( z <-5.13)

                = 1 – 0

= 1

             Answer : 1

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