The answer is 13. im going to also put the picture of the students project that

Question

The answer is 13. im going to also put the picture of the students project that the teacher posted online for the correct work. please explain better than that.

An examination paper consists of twenty questions in each of which the candidate is required to tick as correct one of the three possible answers. Assume that a candidate‘s knowledge about any question may be represented as either ti) complete ignorance in which case he ticks at random or. (ii) complete knowledge in which case he ticks the correct answer. How many questions should a candidate be required to answer correctly if not more than 1 per cent of candidates who do not know the answer to any question are to be allowed to pass? (Use the normal

approximation to the binomial distribution.) *******The answer is 13 questions*****

Explanation / Answer

For the cumulative probabilty that 99% of students are not allowed to pass, z can be found as 2.33 from normal tables.

Now,

Mean,u = 20/3 = 6.66 (20 question with 1/3rd probability)

Standard deviation ,s =sqrt(npq) where n=20,p=1/3 and q=1-p=2/3

s=sqrt(20*1/3*2/3) = 2.108

Now z = (x-u+0.5)/s a factor of 0.5 is added to fix for binomial distribution to normal approximation.

so,2.33 = (x-6.66+0.5 ) / 2.108 This gives x as 12.079

Now, we round up because we want people to not pass and should err on the side of caution.

Hence,x=13 and 13 questions should be the passing marks

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