CFA Institute CFA Institute Certifications CFA-LEVEL-1 Questions & Answers

• Question 3411:

  Which of the following is/are true?

  I. There are as many values above the median as below it.

  II. The sum of the differences between the observations in a sample and the median of the sample equals zero.

  III. The median is greatly affected by "outliers."

  IV.

  A sample has a unique median.

  A.

  II and IV

  B.

  I, II and IV

  C.

  I only

  D.

  II only

  E.

  I and IV

  F.

  III only

  G.

  IV only

  H.

  I, III and IV

  Correct Answer: E

  By definition, there are as many values above the median as below it. Each sample has a unique median.

  (II) and (III) hold for the mean, not for the median.

• Question 3412:

  If you deposit $150 a month, beginning next month, for 20 years into an account paying 6% per year, compounded monthly, how much is in your account after the last deposit?

  A. $70,343.82

  B. $48,833.09

  C. $49,904.67

  D. $143,582.01

  E. $69,306.13

  Correct Answer: E

  On the BAII Plus, press 240 N, 6 divide 12 = I/Y, 0 PV, 150 PMT, CPT FV. On the HP12C, press 240 n, 6 ENTER 12 divide i, 0 PV, 150 PMT, FV. On the BAII Plus, make sure the value of P/Y is set to 1. Note that the answer is displayed as a negative number.

• Question 3413:

  The joint probability of events A and B occurring equals 0.11. The probability of neither A nor B occurring equals 0.64. If P(A) equals 0.24, the probability of B occurring equals ________.

  A. 0.46

  B. 0.29

  C. 0.51

  D. 0.23

  Correct Answer: D

  We are given that P(neither A nor B) = 0.64, P(A and B) = 0.11 and P(A) = 0.24. The probability of neither A nor B occurring equals one minus the probability of either A or B occurring i.e. P(neither A nor B) = 1 - P (A or B).

  Thus, P(A or B) = 1 - P(neither A nor B) = 1 - 0.64 = 0.36.

  Now, P(A or B) = P(A) + P(B) - P(A and B)

  Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.36 - 0.24 + 0.11 = 0.23.

• Question 3414:

  Suppose the probability that oil prices will rise any given quarter is 0.51, and the probability that oil prices will stay level or decline is 0.49. If oil prices rise, GNP will contract by 1% with 80% probability, and expand by 0.5% with 20% probability. If oil prices decline or stay level, GNP will expand 3% with a 75% probability and contract 0.5% with a 25% probability. What is the expected change in GNP in the next quarter?

  A. +0.68%

  B. -0.86%

  C. +0.86%

  D. -0.68%

  Correct Answer: A

  We need the total probability rule for expected value, for which the formula is E(X) = E(X | S_1) * P(S_1) + E(X |S_2) * P(S_2) + ... + E(X |S_n) * P(S_n). Here, E(X) is the expected change in GNP. S_1 is the event that oil prices rise, and S_2 is the event that oil prices fall. Therefore, E(X) = 0.51 * (- 1%*80% + 0.5% *20%) + 0.49 * (3%*75% - 0.5%*25%) = 0.68%, an expansion.

• Question 3415:

  If you already have $500 in a savings account, how much must you deposit 4 years from now in order to have $5,000 in 8 years, assuming the account earns interest at 10% per year, compounded annually?

  A. $4,500.00

  B. $732.05

  C. $2,683.02

  D. $3,415.07

  E. $2,332.54

  Correct Answer: C

  The way to approach this question is to find the PV today of the $5,000 amount, determine the difference

  between this PV and the existing $500 amount in the account, and then move this difference out to the 4

  year from now point. On the BAII Plus, press 8 N, 10 I/Y, 0 PMT, 5000 FV, CPT PV. Then press + 500 =.

  Then press PV, 4 N, CPT FV to see the answer. On the HP12C, press 8 n, 10 i, 0 PMT, 5000 FV, PV.

  Then press 500 +. Then press PV, 4 n, FV to see the answer.

  Make sure the BAII Plus has the P/Y value set to 1.

• Question 3416:

  In an investment environment, an initial outlay of $1 grows to $1.23 in 3 years. If you are expecting a cash inflow of $500 in 3 years, what's the present value of the cash flow to you?

  A. $431.2

  B. $452.25

  C. $406.5

  D. $615

  Correct Answer: C

  The discount factor for 3 years is 1/1.23. Hence, the PV of $500 in 3 years is 500/1.23 = 406.5.

• Question 3417:

  The median and the mode of the sample: 3, 2, 4, 5, 6, 99, 99, 100 equal:

  A. 99, 6

  B. 6, 99

  C. 5, 99

  D. 5.5, 99

  Correct Answer: D

  The mode equals the most common observation; in this case, it is 99.

  If the number of observations is even, the median is the mean of the two middle observations. In this

  dataset, arrange the data in ascending order and select the 4th and 5th observations. These happen to be

  5 and 6. The median is then 5.5.

• Question 3418:

  What is the proportion of the total area under the normal curve within plus and minus two standard deviation?

  A. 68%

  B. 95%

  C. 99.7%

  D. None of these answers are correct

  E. 34%

  Correct Answer: B

  95% of the area under the curve lies within plus and minus one standard deviation of the mean.

• Question 3419:

  Given the following points: (-2, 0), (-1,0), (0,1), (1, 1) and (2, 3) What is the slope of the regression line?

  A. None of these answers

  B. 0.6

  C. 0.0

  D. 0.5

  E. 0.7

  Correct Answer: E

  For this, you need to create tables with columns for X,Y,XY,X^2,Y' and Y-Y'. This will be as follows.

  XYXY X^2 Y'Y-Y'

  -2004-0.40.4

  -10010.3-0.3

  010010

  11111.7-0.7

  23642.40.6

  Sum057100

  N=5.

  The regression equation is Y' = a + bX.

  Then to find the slope, which is b, use the formula

  b = [n(SXY)-(SX)(SY)]/[n(SX^2)-(SX)^2] where here S stands for "Sum of." b = [5(0)-(0)(5)]/[5(10)-0] = 0.7

• Question 3420:

  Which of the following statements regarding confidence levels and/or tests of significance is/are false? Choose the best answer.

  A. In most hypothesis tests, the significance level is set equal to 0.10, 0.05, or 0.01.

  B. All else equal, the probability of a Type I error decreases as the level of confidence increases.

  C. The probability of a Type I error is denoted by the Greek letter alpha.

  D. The confidence level of a hypothesis test can be found by subtracting the level of significance from the number one.

  E. More than one of these answers is false.

  F. The significance level of a test is equal to the power of a test.

  Correct Answer: F

  Remember that the power of the test is equal to (1 - Type II error probability). This is because in most hypothesis tests, the level of significance, denoted by alpha, is set equal to the probability of a Type I error. Statisticians are primarily concerned with the probability of a Type I error, and rarely specify the probability of a Type II error. Determining the probability of a Type II error, which is defined as the act of incorrectly failing to reject the null hypothesis, is inherently difficult to determine. The probability of a Type I error, however, can be determined with relative ease. A Type I error is defined as the act of incorrectly rejecting the null hypothesis. The remaining answers are all correct.