Q: A savings account offers a 4% annual interest rate compounded quarterly. Which formula would you use to find the future value $$A$$ after $$5$$ years if you deposit $$\2$$,000$?

$$A = 2000 \left(1 + \frac{0.04}{4}\$$right)^{4 \times 5}$$

Question 1

Which formula should you use to calculate the future value $$F of a $$principal $$P$$ invested at a simple interest rate $$r$$ for $$t$$ years?

Accepted Answer

$$F = P(1 + rt)$$

Question 2

A savings account offers a 4% annual interest rate compounded quarterly. Which formula would you use to find the future value $$A$$ after $$5$$ years if you deposit $$\2$$,000$?

Accepted Answer

$$A = 2000 \left(1 + \frac{0.04}{4}\$$right)^{4 	imes 5}$$

Question 3

Which of the following best describes the difference between permutations and combinations?

Accepted Answer

Permutations consider order, while combinations do not.

Question 4

A survey of 100 students found that 60 like coffee, 50 like tea, and 20 like both. How many students like only coffee?

Accepted Answer

$$60 - 20 = 40$$

Question 5

If the mean of a data set is $$50$$ and the standard deviation is $$5$$, what is the $$z-$$score for a value of $$60$$?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 6

Which voting method awards points based on the ranking of candidates by each voter?

Accepted Answer

Borda Count

Question 7

A loan of $$\10$$,000$$ is to be repaid in equal monthly payments over 5 years at an annual interest rate of 6% compounded monthly. Which formula would you use to find the monthly payment $$PMT$?

Accepted Answer

$$PMT = \frac{10000 \cdot 0.06/12}{1 - (1 + 0.06/12$$)^{-60}$$}$$

Question 8

Which of the following is NOT a criterion for fairness in voting methods?

Accepted Answer

Quota Criterion

Question 9

If a set $$A = \{1, 2, 3, 4\}$$ and set $$B = \{3, 4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 4\}$$

Question 10

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

$$\frac{3}{10}$$

Question 11

Which apportionment method can result in the Alabama Paradox, where increasing the total number of seats causes a state to lose a seat?

Accepted Answer

Hamilton's Method

Question 12

If the odds in favor of an event are 3 to 2, what is the probability of the event occurring?

Accepted Answer

$$\frac{3}{5}$$

Question 13

A data set has the following values: $$2, 4, 4, 6, 8. $$What is the median?

Accepted Answer

$$4$$

Question 14

Which of the following best describes the 68–95–99.7 rule for normal distributions?

Accepted Answer

About 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

Question 15

A committee of 4 is to be chosen from 10 people. How many different committees are possible?

Accepted Answer

$$\binom{10}{4} = 210$$

Question 16

Which of the following is a real-world example of using the Fundamental Counting Principle?

Accepted Answer

Calculating the number of possible meal combinations at a restaurant with 3 appetizers, 4 main courses, and 2 desserts: $$3 	imes 4 	imes 2$$

Question 17

If $$A$$ and $$B$$ are independent events with $$P(A) = 0.4$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 18

Which of the following is an example of a conditional probability?

Accepted Answer

The probability that a student passes math given that they attended all classes.

Question 19

Which measure of central tendency is most affected by extreme values (outliers)?

Accepted Answer

Mean

Question 20

A state’s population increases, but its number of seats in the House of Representatives decreases after apportionment. This is an example of which paradox?

Accepted Answer

Population Paradox

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