Question

A quiz in Microeconomics has 40 multiple answer questions and each of them has 4 possible answers, but only one of them is correct. For every correctly answered question a student gets 15 points and for every incorrectly answered she loses 5 points. What is the probability of passing the quiz (the minimum required is 120 points) if a student is randomly picking the answers? (hint: you may use a normal approximation)

Answer 1

Sol Given that, A quiz in Microeconomics has 40 multiple answer questions and each of them has 4 possible answers. only one of them correct. A student gets is points for correctly answered question and loses 5 points for incorrectly answered question. 120 for quiz, the minimum required passing the points. let 'k be the cament number of questions answered 15e student. correctly by So, '40-4' answered incorrectly are Since 120 points is minimum required pams quiz , k * 15 + (40-6)* (-5) 7120 isk 200 +5k7 120 zok - 2007 120 2ok 7 320 k z 16 So, the student student correctly answer minimum of 16 questions.

Since the student randomly picks the probability of answering correctly = 1 = 0.25 Mear, M = up= (40) (0.25 =10 answers, 15e let x be random variable denotes the number of questions correctly answered by the student out of 40 n=40 þ= 0.25 XN Binomial (n=40, p=0.25) Here, np=(40) (0.25)= 10 nci-p) = (40) (1-0.25)= 30 Since np>s and aCl-p)75, we can use normal approximation for the Binomial distribution. So Binomial can be approximated to normal with, Standard deviation, sa Sup (1-p) = √(40) 10.25) (1-0.25) ł 2.7386 . X~ N(p=10,0 = 2.7386) Here, we need to find P(x>, 16) P(x7, 16) P(x> 15.5) [By using Continuity correction p(x-> 2.7386 P(Z > 2.008) - P(Z 22.008) = 1- 0.977678 [from standard 0.02232 Normal table ~0.6223 15.5-10

Answer 2

Quantity 1 2 3 4 5 6 7

Firm A $60 $70 $80 $90 $100 $110 $120

Firm B 11 24 39 56 75 96 119

Firm C 21 34 49 66 85 106 129

Does each of these firms experience economies

of scale or diseconomies of scale?