Q: A savings account offers a simple interest rate of $$4\%$$ per year. If you deposit $$\2$$,000$, how much interest will you earn in 3 years?

$$I = P \times r \times t = 2000 \times 0.04 \times 3 = \240$

Q: A population of bacteria doubles every 6 hours. If there are initially $$500$$ bacteria, how many will there be after 24 hours?

$$N = 500 \times 2$$^{24/6}$$ = 500 \times 2^4$ = 500 \times 16 = 8000$$

Q: A deck of 52 cards is shuffled. What is the probability of drawing a heart or a king?

$$P(\text{heart}) + P(\text{king}) - P(\text{king of hearts}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Q: A bag contains 5 red, 3 blue, and 2 green marbles. If you draw one marble at random, what is the probability it is not blue?

$$P(\text{not blue}) = 1 - \frac{3}{10} = \frac{7}{10}$$

Q: A student rolls two fair six-sided dice. What is the probability that the sum is 7?

$$P(\text{sum}=7) = \frac{6}{36} = \frac{1}{6}$$

Q: A loan of $$\10$$,000$$ is taken out at an annual interest rate of 6$$\%$$ compounded annually for 5 years. What is the total amount owed at the end of 5 years? (Use A = P(1 + r)^t$)

$$A = 10,000 \times (1 + 0.06)^5$ = 10,000 \times 1.3382 = \13$$,382$

Q: If a normal distribution has a mean of $$100$$ and a standard deviation of $$15$$, what percentile is a score of $$115$$? (Use the standard normal table.)

$$z = \frac{115 - 100}{15} = 1$$, \text{which corresponds to the 84th percentile}$

Q: A city’s population grows exponentially at a rate of $$3\%$$ per year. If the current population is $$200,000$$, what will the population be in 10 years? (Use $$P = P_0$ e$$^{rt}$$)

$$P = 200,000 \times e$$^{0.03 \times 10}$$ = 200,000 \times e$$^{0.3}$$ \approx 200,000 \times 1.3499 = 269,980$$

Question 1

A hospital reports that the number of flu cases increased from 120 last month to 180 this month. What is the relative change in the number of cases?

Accepted Answer

$$\frac{180 - 120}{120} = 0.5 or$$ $$50\%$$

Question 2

Convert $$0.375 to a $$fraction and a percentage.

Accepted Answer

$$\frac{3}{8}$$ and $$37.5\%$$

Question 3

A savings account offers a simple interest rate of $$4\%$$ per year. If you deposit $$\2$$,000$, how much interest will you earn in 3 years?

Accepted Answer

$$I = P 	imes r 	imes t = 2000 	imes 0.04 	imes 3 = \240$

Question 4

A population of bacteria doubles every 6 hours. If there are initially $$500$$ bacteria, how many will there be after 24 hours?

Accepted Answer

$$N = 500 	imes 2$$^{24/6}$$ = 500 	imes 2^4$ = 500 	imes 16 = 8000$$

Question 5

Which of the following is the correct scientific notation for $$0.00056$$?

Accepted Answer

$$5.6 	imes 10$$^{-4}$$

Question 6

A deck of 52 cards is shuffled. What is the probability of drawing a heart or a king?

Accepted Answer

$$P(	ext{heart}) + P(	ext{king}) - P(	ext{king of hearts}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$

Question 7

Given the data set: $$[2, 4, 4, 7, 9, 10, 10, 10, 12]$$, what is the mode?

Accepted Answer

$$10$$

Question 8

A bag contains 5 red, 3 blue, and 2 green marbles. If you draw one marble at random, what is the probability it is not blue?

Accepted Answer

$$P(	ext{not blue}) = 1 - \frac{3}{10} = \frac{7}{10}$$

Question 9

A student rolls two fair six-sided dice. What is the probability that the sum is 7?

Accepted Answer

$$P(	ext{sum}=7) = \frac{6}{36} = \frac{1}{6}$$

Question 10

A data set has a mean of $$50$$ and a standard deviation of $$8. $$What is the $$z-$$score for a value of $$66$$?

Accepted Answer

$$z = \frac{66 - 50}{8} = 2$$

Question 11

A frequency table shows the following number of books read by students in a month: 0 books (5 students), 1 book (8 students), 2 books (12 students), 3 books (10 students), 4 books (5 students). What is the median number of books read?

Accepted Answer

2

Question 12

A loan of $$\10$$,000$$ is taken out at an annual interest rate of 6$$\%$$ compounded annually for 5 years. What is the total amount owed at the end of 5 years? (Use A = P(1 + r)^t$)

Accepted Answer

$$A = 10,000 	imes (1 + 0.06)^5$ = 10,000 	imes 1.3382 = \13$$,382$

Question 13

A boxplot shows a data set with a minimum of 10, first quartile (Q1) of 15, median of 20, third quartile (Q3) of 25, and maximum of 40. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 25 - 15 = 10$$

Question 14

If a normal distribution has a mean of $$100$$ and a standard deviation of $$15$$, what percentile is a score of $$115$$? (Use the standard normal table.)

Accepted Answer

$$z = \frac{115 - 100}{15} = 1$$, 	ext{which corresponds to the 84th percentile}$

Question 15

A city’s population grows exponentially at a rate of $$3\%$$ per year. If the current population is $$200,000$$, what will the population be in 10 years? (Use $$P = P_0$ e$$^{rt}$$)

Accepted Answer

$$P = 200,000 	imes e$$^{0.03 	imes 10}$$ = 200,000 	imes e$$^{0.3}$$ \approx 200,000 	imes 1.3499 = 269,980$$

Question 16

A researcher records the following data: $$[8, 12, 15, 20, 25]. $$What is the mean of the data set?

Accepted Answer

$$\frac{8 + 12 + 15 + 20 + 25}{5} = \frac{80}{5} = 16$$

Question 17

A savings account compounds interest monthly at an annual rate of $$2\%. If $$you deposit $$\1$$,000$$, how much will you have after 2 years? (Use A = P(1$$ + \frac{r}{n}$$)^{nt}$$, where $$n=12$)

Accepted Answer

$$A = 1000 	imes (1 + \frac{0.02}{12}$$)^{12 	imes 2}$$ = 1000 	imes (1.0016667$$)^{24}$$ \approx 1000 	imes 1.0407 = \1$$,040.74$

Question 18

A company’s revenue increased from $$\1.2$ million to $$\$$1.5$$ million in one year. What is the absolute change?

Accepted Answer

$$1.5 - 1.2 = 0.3$$ million dollars

Question 19

A student wants to convert $$3.2 	imes 10^5$ to standard decimal notation. What is the correct answer?

Accepted Answer

$$320,000$$

Statistics Study Notes: Data Description, Probability, and Financial Applications

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