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

• Question 3321:

  If alpha = .05, what is the probability of making a Type I error?

  A. None of these answers

  B. 20/20

  C. 0

  D. 19/20

  E. 1/20

  Correct Answer: E

  Alpha is the probability of committing a type I error. So 0.05 = 1/20.

• Question 3322:

  The p-value in hypothesis testing:

  A. equals the significance level.

  B. is less than the probability of type I error.

  C. equals the probability of type II error.

  D. none of these answers.

  Correct Answer: D

  The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level. None of the choices fit this definition of the p-value.

• Question 3323:

  You are running a year-end bonus pool for your top credit analysts. You have 10 analysts, and you wish to recognize the top 3. How many different possible outcomes are there, if all three get the same bonus? How many different outcomes are there if the top analyst gets 50% of the bonus pool, the second best analyst gets 30%, and the third best gets 20%?

  A. 720; 720.

  B. 720; 120.

  C. 120; 720.

  D. 120; 120.

  Correct Answer: C

  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)!]. In this case, we have (10 choose 3) = 10! / [3! * 7!] = (10

  * 9 * 8) / (6) = 120. In the second case, where the order chosen does matter, we need the general permutation formula, which gives the number of ways that k objects can be chosen from n items, with regard to order. The formula is n_P_k = n! / (n- k)!. Here, it is 10! / (10-3)! = 720. For permutations, we don't consider choosing analysts 3, 7, and 6 the same as choosing analysts 7, 3, and 6, so there are more combinations than under the combination formula.

• Question 3324:

  If you deposit $10,000 into an account paying 6% per year, compounded semiannually, how much do you have in the account in 10 years?

  A. $15,403.52

  B. $18,061.11

  C. $18,938.48

  D. $21,667.70

  E. $17,800.00

  Correct Answer: B

  On the BAII Plus, press 20 N, 6 divide 2 = I/Y, 10000 PV, 0 PMT, CPT FV. On the HP12C, press 20 n, 6 ENTER 2 divide i, 10000 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 3325:

  An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.

  Weight % of Total Underweight 2.5 Satisfactory 90.0 Overweight 7.5

  Three packages are selected from the food processing line. What is the probability of selecting and finding that all three of them are satisfactory?

  A. 0.900

  B. 0.075

  C. 0.729

  D. 0.810

  E. None of these answers

  Correct Answer: C

  P(all three satisfactory) = 0.9*0.9*0.9 = 0.729.

• Question 3326:

  If you deposit $300 a month, beginning next month, for 10 years into an account paying 8% per year, compounded monthly, how much is in your account after that last deposit?

  A. $38,444,973.53

  B. $30,000.00

  C. $54,883.81

  D. $3,091.62

  E. $58,402.98

  Correct Answer: C

  On the BAII Plus, press 120 N, 8 divide 12 = I/Y, 0 PV, 300 PMT, CPT FV. On the HP12C, press 120 n, 8 ENTER 12 divide i, 0 PV, 300 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 3327:

  The sum of the squares of 1,200 observations equals 9,830. The sum of the observations equals 1,510. The population standard deviation of the observations equals ________.

  A. 4.22

  B. 2.57

  C. 5.31

  D. 6.61

  Correct Answer: B

  For N observations, it is easy to show that

  population variance*N = (sum of squares) - N*(mean^2)

  The mean equals 1,510/1,200 = 1.258. Hence, population variance = (9,830 - 1,200*1.258^2 )/1,200=

  6.608. The standard deviation then equals sqrt(6.608) = 2.57

  Note: You should be careful about the difference between population variance and sample variance. The formula for sample variance is:

  sample variance*(N-1) = (sum of squares) - N*(mean^2)

  You can expect an exam question which asks for population variance, with the choices given containing both the population and the sample variances or vice versa.

• Question 3328:

  You are examining a group of 20 mutual funds. You find that 5 have an 8% position in foreign stocks, 7 have a 9% position in foreign stocks, and 8 have no position in foreign stocks. What is the weighted average position in foreign stocks of these 20 mutual funds?

  A. 5.10%.

  B. 5.20%.

  C. 5.25%.

  D. 5.15%.

  Correct Answer: D

  A weighted-average is equal to the sum (as i goes from 1 to n) of w_i * X_i, where w_i is the percentage weight of the ith item, and X_i is the value of the ith item. Here, we get a weighted mean of 5/20 * 0.08 + 7/20 * 0.09 + 8/20 * 0 = 5.15%.

• Question 3329:

  What annual interest rate, compounded annually, would cause a series of 10 deposits of $1,000 to accumulate to $18,000, if the first deposit is made one year from today?

  A. 14.49%

  B. 12.52%

  C. 12.69%

  D. 11.84%

  E. 35.82%

  Correct Answer: B

  On the BAII Plus, press 10 N, 0 PV, 1000 PMT, 18000 +/- FV, CPT I/Y. On the HP12C, press 10 n, 0 PV, 1000 PMT, 18000 CHS FV, i. Make sure that the BAII Plus has the P/Y value set to 1.

• Question 3330:

  What is the remaining balance on a $90,000 loan after making monthly payments of $660.39 for 10 years, if the interest rate is 8% per year, compounded monthly?

  A. $51,948.80

  B. $81,343.92

  C. $0

  D. $76,204.11

  E. $78,951.89

  Correct Answer: E

  On the BAII Plus, press 120 N, 8 divide 12 = I/Y, 90000 PV, 660.39 +/- PMT, CPT FV. On the HP12C, press 120 n, 8 ENTER 12 divide i, 90000 PV, 660.39 CHS PMT, FV. The remaining balance will be displayed as a negative number. Make sure the BAII Plus has the P/Y value set to 1.