An examination paper consists of twenty questions each of which in the candidate

Question

An examination paper consists of twenty questions each of which in 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 (i) 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.)

Explanation / Answer

Solution:

we want to set the passing mark for those who are purely guessing.
the binomial distribution has n = 20, p = 1/3, q = 2/3

mean = np = 20/3 = 6.667
SD = sqrt(npq) = sqrt(20*1/3*2/3) = 2.108
z-value for a right tail of 1% = 2.326,
so reqd. passing score = 6.667 + 2.326*2.108 = 11.57

the rounding up could have the following explanation
12 in the continuous normal distribution means 11.5 to 12.5
to be sure that < = 1% of "guessers" pass,
we must round up the passing mark to 13

or else a countercheck is supposed to be made afterwards !
the exact binomial gives a probability of 1.3% with 12
and 0.37% with 13

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.