Q: Which of the following is the correct formula for calculating the percentage change from an old value to a new value?

$$\frac{\text{new value} - \text{old value}}{\text{old value}} \times 100\%$$

Q: A company’s revenue grew from $$50,000 to 65$$,000 in one year. What is the percentage increase in revenue?

$$\frac{65,000 - 50,000}{50,000} \times 100\% = 30\%$$

Q: A business invests $$\5$$,000$$ at an annual interest rate of 4$$\%$ compounded annually. What will be the value after 3 years?

$$5,000 \times (1 + 0.04)^3$ = 5,624.32$$

Q: A sequence is defined by $$a_n = 2a_{n-1} + 3$$, with $$a_1 = 1$. What is a_3$?

$$a_2 = 2$$ \times 1 + 3 = 5$$, a_3$ = 2 \times 5 + 3 = 13$$

Question 1

A business analyst is evaluating the impact of a new marketing strategy. She wants to determine if there is a causal relationship between advertising spend and sales increase. Which of the following best describes the difference between correlation and causation in this context?

Accepted Answer

Correlation means there is a statistical association between advertising spend and sales increase, but causation means advertising spend is the direct reason for sales increase.

Question 2

A company wants to compare the average monthly sales of two products. The sales data for Product A are: $$10,000, 12,000, 11,000, 13,000, 12,500. $$What is the mean sales for Product A?

Accepted Answer

$$\frac{10,000 + 12,000 + 11,000 + 13,000 + 12,500}{5} = 11,700$$

Question 3

Which of the following statements about the normal distribution is correct?

Accepted Answer

The mean, median, and mode of a normal distribution are all equal.

Question 4

A student scored 1.5 standard deviations above the mean on a statistics exam. If the mean score is 70 and the standard deviation is 8, what was the student's score?

Accepted Answer

$$70 + (1.5 	imes 8) = 82$$

Question 5

A mortgage has an annual interest rate of 6\% compounded monthly. What is the monthly interest rate?

Accepted Answer

$$\frac{6\%}{12} = 0.5\%$$

Question 6

Which of the following is the correct formula for calculating the percentage change from an old value to a new value?

Accepted Answer

$$\frac{	ext{new value} - 	ext{old value}}{	ext{old value}} 	imes 100\%$$

Question 7

A business owner wants to visualize the distribution of monthly expenses. Which type of graph is most appropriate for showing the frequency of different expense categories?

Accepted Answer

Bar chart

Question 8

If the odds of winning a prize are 3 to 7, what is the probability of winning?

Accepted Answer

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

Question 9

A company’s revenue grew from $$50,000 to 65$$,000 in one year. What is the percentage increase in revenue?

Accepted Answer

$$\frac{65,000 - 50,000}{50,000} 	imes 100\% = 30\%$$

Question 10

Which of the following is NOT a valid argument in logic?

Accepted Answer

If it rains, then the ground gets wet. The ground is wet. Therefore, it rained.

Question 11

A dataset has the following values: $$2, 4, 4, 8, 10. $$What is the median?

Accepted Answer

$$4$$

Question 12

Which formula correctly calculates the standard deviation for a sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

$$\sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2$}{n-1}}$$

Question 13

A business invests $$\5$$,000$$ at an annual interest rate of 4$$\%$ compounded annually. What will be the value after 3 years?

Accepted Answer

$$5,000 	imes (1 + 0.04)^3$ = 5,624.32$$

Question 14

Which of the following best describes a contrapositive statement?

Accepted Answer

If not Q, then not P.

Question 15

A company tracks the number of defective products each month: $$3, 5, 2, 4, 6. $$What is the mode?

Accepted Answer

There is no mode.

Question 16

Which of the following is the correct formula for simple interest?

Accepted Answer

$$I = P 	imes r 	imes t$$

Question 17

A business manager uses Excel to calculate the average sales for the last 12 months. Which Excel function should she use?

Accepted Answer

AVERAGE()

Question 18

A sequence is defined by $$a_n = 2a_{n-1} + 3$$, with $$a_1 = 1$. What is a_3$?

Accepted Answer

$$a_2 = 2$$ 	imes 1 + 3 = 5$$, a_3$ = 2 	imes 5 + 3 = 13$$

Question 19

A survey found that 60\% of customers prefer Product X, 30\% prefer Product Y, and 10\% prefer Product Z. If 200 customers were surveyed, how many preferred Product Y?

Accepted Answer

$$200 	imes 0.3 = 60$$

Statistics for Business: Course Syllabus Overview

Guida di studio - Domande di pratica

Study guide - Flashcard