Problem 1(13pts) A student is studying for the test which has 40 questions. Each

Question

Problem 1(13pts) A student is studying for the test which has 40 questions. Each question is a multiple choice question with 6 options. The student studied 25% of the content of the test. The rest of the test he will randomly pick the answer. We assume that students answered correctly al the questions he or she studied.

(1pt) Find P(Score=5).

(2pts) Find P(Score=30).

(2pts) Find P(Score=k).

(3pts) What should the student expect to be his score on the test?

(2pts) Another student scored 25 on the test. What is the expected value of the material the student studied?

(3pts) 100 students took the test. The average test score was 30 with standard deviation of 4. Find 95% confidence interval for the amount of material (in percentage) the students studied?

Explanation / Answer

As the student has studied 25%, we expect him to answer the 25% of 40 questions, that is, 10 questions are answered perfectly and of the remaining 30 questions as he randomply picks one of 6 options, he has a probability of getting the right answer as 1/6.

(A)   (1pt)   Find P(Score = 5)   Is this 1 or 0? Since we expect the student to answer at least 10 questions correctly

so it should be 0 as we are talking about exact probability here if it is asked that P(score>5) then it would be 1.

(B)   (2pts) Find P(Score = 30) = it would be when student will get 20 marks out of 30 unknown questions.

so P( score = 30) = 30C20 * (1/6)20 * (5/6)10 this value is less than 0.0001 so it is about to be 0.

(C)   (2pts) Find P(Score = k)   =  30Ck-10 * (1/6)k-10 * (5/6)40-k   when 10 <= k <= 30

(D)   (3pts) What should student expect for his score?   10+()*30 = 15

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