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

• Question 3471:

  Sweetwater and Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

  A. 0.0164

  B. 0.0001

  C. 0.8187

  D. 0.2500

  E. None of these answers

  Correct Answer: A

  This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(p^r)[q^(n-r)]/r! (n-r)!. Here n = 400, r = 2,p = 0.0005 and q = 0.9995. Therefore we have 400!(0.0005^2) (0.9995^398)/2!398! = 0.0164.

• Question 3472:

  A bell-shaped, symmetrical frequency distribution has a mean of 10. If 16% of the observations in the distribution are negative, what is the coefficient of variation of X?

  A. 1.0

  B. 0.32

  C. 10.0

  D. 0.1

  Correct Answer: A

  The fraction of observations which are less than zero equals 16% i.e. the fraction of observations which are less than (mean - 10) equals 16% (given). Since the distribution is symmetrical about the mean, this implies that the fraction of observations which are more than (mean + 10) also equals 16%. Thus, the fraction of the observations lying between 0 and 20 equals 1-0.16-0.16 = 0.68. For a bellshaped, symmetrical frequency distribution, 68% of the observations lie within one standard deviation of the mean. Hence, the standard deviation of the distribution equals 10. The coefficient of variation is then equal to standard deviation/mean = 10/10 = 1.

• Question 3473:

  A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?

  A. About 4

  B. None of these answers

  C. About 40

  D. About 100

  E. About 16

  Correct Answer: A

  Population variance = (Sum of squared deviation from the mean)/N. The mean is 210. Population variance = (36 + 25 + 9 + 4 + 16 + 4)/6 = 94/6 = 15.67. Population standard deviation is the square root of the population variance = 3.958. xx-mean(x-mean)^2 204-636 215525 207-39 21224 214416 208-24

• Question 3474:

  You are faced with a counting problem in which you must choose k objects from n total objects. The order of choosing does not matter. The counting method you should use is:

  A. None of these answers is correct.

  B. The binomial formula.

  C. The multinomial formula.

  D. The multiplication rule.

  Correct Answer: B

  The combination, or binomial formula, gives the number of ways that k objects can be chosen from n items, without regard to the order of choosing. The formula is n_C_k = (n choose k) = n! / [k! *(n-k)!].

• Question 3475:

  In a statistical regression estimation, the R-square is found to be 39% and the slope coefficient is -0.3. The percentage of variance of the dependent variable not explained equals ________.

  A. 0.30

  B. 0.61

  C. 0.09

  D. 0.39

  Correct Answer: B

  The R-square of the regression measures the amount of variance of the dependent variable explained by the independent variable. This is given to be 39%. Hence, the amount not explained equals 100% - 39% = 61%.

• Question 3476:

  If you deposit $400 today into an account paying 8% per year, compounded quarterly, how much will be in the account after 42 months?

  A. $10,135.79

  B. $1,174.88

  C. $918.90

  D. $927.54

  E. $527.79

  Correct Answer: E

  There are 14 quarters in 42 months (42 divide 3 =). On the BAII Plus, press 14 N, 8 divide 4 = I/Y, 400 PV, 0 PMT, CPT FV. On the HP12C, press 14 n, 8 ENTER 4 divide i, 400 PV, 0 PMT, FV. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.

• Question 3477:

  A market survey was conducted to estimate the proportion of homemakers who could recognize the brand name of a cleanser based on the shape and color of the container. Of the 1,400 homemakers, 420 were able to identify the brand name. Using the 0.99 degree of confidence, the population proportion lies within what interval?

  A. 0.250 and 0.350

  B. 0.268 and 0.332

  C. 0.950 and 0.997

  D. 0.100 and 0.400

  E. None of these answers

  Correct Answer: B

  Interval estimate can be found from p +/- z[p(1-p)/n]^0.5. Here we have n = 1400, p = 414/1400 = 0.3 and z = 2.58 (for 99%).

  Therefore 0.3 +/- 2.58*0.01225 and we get 0.268 and 0.332.

• Question 3478:

  What annual interest rate, compounded annually, would cause a series of 10 deposits of $500 to accumulate to $9,000, if the first deposit is made one year from today?

  A. 12.52%

  B. 15.38%

  C. 11.12%

  D. 8.04%

  E. 10.09%

  Correct Answer: A

  On the BAII Plus, press 10 N, 0 PV, 500 PMT, 9000 +/- FV, CPT I/Y. On the HP12C, press 10 n, 0 PV, 500 PMT, 9000 CHS FV, i. Make sure the BAII Plus has the P/Y value set to 1.

• Question 3479:

  How much would you need to deposit today in order to be able to withdraw $500 in 2 years and $700 in 4 years, if the account has nothing in it today and interest is 6% per year, compounded annually?

  A. $999.46

  B. $1,007.54

  C. $445.00

  D. $1,200.00

  E. $950.51

  Correct Answer: A

  Work this question as two compound interest problems. On the BAII Plus, press 2 N, 6 I/Y, 0 PMT, 500 FV, CPT PV, which yields $445.00. Then press STO 1. Then press 4 N, 700 FV, CPT PV, which yields $554.46. Then press + RCL 1 = to see the answer. On the HP12C, press 2 n, 6 i, 0 PMT, 500 FV, PV. Then press STO 1. Then press 4 n, 700 FV, PV. Then press RCL 1 + to see the answer. Note that the answer will be displayed as a negative number.

• Question 3480:

  You have invested in a long-term, fixed deposit account earning 4% per year for 20 years, compounded annually. Your friend has invested in a similar account but one that earns 4.25% per year, compounded semi-annually. If each of you deposited $5,000, by what amount is your friend wealthier than you due to this deposit?

  A. $538

  B. $601

  C. $639

  D. $521

  Correct Answer: C

  The friend's account has 5,000*(1+0425/2)^40 = 11,595 at the end of 20 years. Your account has 5,000* (1.04^20) = 10,956. The difference is $639.