A random variable X is normally distributed with a mean of 1 and variance 4. Find a) The probability that a randomly selected score from this distribution is less than 3.

a.)Sketch a normal curve and shade out the region.

b) The probability that a score selected at random from this distribution lies between 2 and 5. Sketch a normal curve and shade out the region

c) The probability that a score selected at random from this distribution is greater than 0. Sketch a normal curve and shade out the region.

1. If reserves decrease by $4 million and the required reserve ratio is 6%, what is the change in the money supply?

2. According to Simple Quantity Theory of Money, what is the change in price level if money supply increases by 20% from $500 and both velocity and quantity are constant, at 2 and 100 respectively?

A bank has made a 1-year loan at 4%. To fund the loan, it issued a 6-month deposit at 2.5%. It also purchased a 6x12 FRA at 3%. On the settlement date of the contract, 6-month LIBOR is 5%, and the bank issues a 6-month deposit at LIBOR. What is the bank’s interest margin (spread), in %, for the first six months and for the next?

1. 1.5% and 1.5%
2. 1.5% and 1%
3. 1.5% and −1%
4. 1% and −1%
5. 1% and 1%
6. 1.5% and 2%

A point charge of -4 micro C is located at x = 1 m, y = -2 m. A second point charge of 12 micro C is located at x = 1 m, y = 3 m.

(a) Find the magnitude and direction of the electric field at x = -1 m, y = 0.

(b) Calculate the magnitude and direction of the force on an electron at x = -1 m, y = 0.

Suppose that apples cost $1. A consumer feels that they are willing to give up 4 apples in order to consume a banana, as long as they are consuming 10 or less bananas. After the 10th banana their appreciation for them is not as high, so they are willing to trade 2 apples for an additional banana, as long as their banana consumption is less than or equal to 20. After the 20th banana they are fed up of bananas and would not give up a single apple for a banana. Note: All parts are worth 10 points.

Questions: (1) What is the demand curve for bananas (a picture, fully labelled, is enough)

(2) Assume the supply curve for bananas is S(p)=5p. What is the equilibrium price and quantity in the market for bananas? (3) Suppose that there is a natural disaster in apple growing countries, so now the price of apples is $2.

Assume that the resources used in banana production are not suitable for apple production, so this change in the price of apples leaves supply of bananas unaffected. What is the new equilibrium price and quantity in the market for bananas?

Question 4 a. Suppose that the annual interest rate is 1% and no dividend will be declared for the index constituent stocks in the coming quarter. The index is currently standing at 25,500.

i. Compute the index futures deliverable in exact 3 months.

ii. Suppose now the dividend yield of the index constituent stocks is 0.3% rather than 0%. Without doing any calculation, explain whether the index futures price is higher or lower than your answer in part (i).

b. A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. Henry sells four July silver futures contract at a price of $16 per ounce. The initial margin is $6,000 per contract and the maintenance margin is $2,500 per contract. What is the futures price per ounce at which Henry would receive a margin call?

QUESTIONS 1 TO 4 ARE BASED ON THE FOLLOWING INFORMATION. Consider the random variable X with a mean 100 and a population standard deviation of 9. Assume a sample of size 30 was used.

Question 1
Consider the statements below.
(A) The 90% confidence interval estimate for the population mean is (97.2970; 102.7030)

(B) The 95% confidence interval estimate for the population mean is (96.7794; 103.2206)

(C) The 99% confidence interval estimate for the population mean is (95.7606; 104.2394)

Which statement(s) are correct?
(1) Only A.
(2) Only B.
(3) Only C.
(4) Only A and B.
(5) A, B and C.

Question 2

Assuming the sample size stays the same, what happens to the confidence interval estimate when the level of confidence increases?
(1) The confidence interval estimate doesn’t change.
(2) The confidence interval estimate becomes wider.
(3) The confidence interval estimate becomes narrower.
(4) The confidence interval estimate converges to zero.
(5) None of the above.

Question 3

Which of the following statements is incorrect?

(1) When the sample size is 60 the 95% confidence interval estimate for the population mean is (97.7227; 102.2773)

(2) When the sample size is 100 the 95% confidence interval estimate for the population mean is (98.2360;  101.7640)

(3) When the sample size is 200 the 95% confidence interval estimate for the population mean is (98.7527; 101.2473)

(4) When the sample size is 500 the 95% confidence interval estimate for the population mean is (99.2111; 100.7889)

(5) None of the above.

Question 4

Assuming the level of significance stays the same, what happens to the confidence interval estimate when the sample size increases?

(1) The confidence interval estimate doesn’t change.
(2) The confidence interval estimate becomes wider.
(3) The confidence interval estimate becomes narrower.
(4) The confidence interval estimate converges to zero.
(5) None of the above.