Question

Rim is not a good student. Her exam strategy is to rely on luck for the next exam. The exam consists of 20 questions. Each question has 5 possible answers, only one of which is correct. Rim plans to guess the answer to each question. Answer the following questions:

1. Using the Binomial Formula, find the probability that Rim gets exactly 6 false answers?

2. What is the probability that Rim gets 5 or more correct answers?

3. What is the expected value of the number of correct answers? What is the standard deviation of the number of wrong answers?

Problem 2:

2. You are given different scenarios for the rates of returns for Intek and Zurick stocks.

Scenario	Probability	Return (Intek)	Return (Zurick)
Boom	0.35	12%	6%
Normal	0.25	2%	4%
Recession	0.4	-4%	-1%

1. What is the probability that returns will be lower or equal to 2% for Intek?

2. What is the probability that returns will be higher than 2% for Intek?

3. What is the probability that returns will be higher than 4% for Zurick?

4. Compute the expected return for each stock.

           

5. Compute the standard deviation of return for each stock

Answer 1

Binomial distribution

the number of wrong Now, The probability Ket x be the random variable denoting the number of connect answers and Y be the nandom vaniable denoting answers. X follows binomial distribution with success probability 1/5 and Y ~ binomial distribution with success proobability 4. mass functions are given by! P(x-x) - ( 2 ) (0.23% (0.8)2 P (NY)= ( 20 ) (0.87% (0.2) 20-y. a) Required probability: PCY=6) ( 23 ) (0.8)0(012)44 = 166 10-6 b) Requined probability: P(x>5) = 1- P(xL5) { P(X-0) +P (x+1)+...+ = 1 - (0.0L * 0.06 +0:14 +0.20 +0.22) 20 -2 2 21- P (x=4)} a 1 - 0.63 - 0.37 Ans

We know that, E(x) = np 20x 0.2 = 4 : Expected value of the number of correct answers is 4 Nar (Y) = npq = nb. (1.b) = 200.8x0.2 = 32 standard deviation (4) - (3.278.5 - 1.79 The standard deviation of the number of wrong numbers as 1.79. Ang is given