Q: A marketing campaign costs $$20,000. If successful (probability 0.4), profit is 80$$,000. If unsuccessful (probability 0.6), loss is $20,000. What is the expected net gain?

$$E = 0.4 \times 60,000 + 0.6 \times (-20,000) = 12,000$$

Q: A call center finds 30% of customers purchase an add-on. If 8 customers are contacted, what is the mean number of purchases?

$$\mu = np = 8 \times 0.3 = 2.4$$

Question 1

A company records the following daily sales (in $1,000s): 18, 22, 15, 30, 25, 20. What is the sample mean of the sales?

Accepted Answer

$$\frac{130}{6}$$

Question 2

Given the same sales data: 18, 22, 15, 30, 25, 20. What is the sample standard deviation? (Round to two decimals)

Accepted Answer

$$5.13$$

Question 3

A student scores 91 on an exam where the mean is 75 and the standard deviation is 8. What is the z-score for this student?

Accepted Answer

$$z = \frac{91-75}{8}$$

Question 4

If a distribution is right-skewed, which of the following is true?

Accepted Answer

The tail is to the right

Question 5

A company’s quarterly profits (in millions) are: 5, 8, 10, 6, 9, 12, 7. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 10 - 6 = 4$$

Question 6

Which Excel function would you use to calculate the sample variance of a dataset?

Accepted Answer

=VAR.S()

Question 7

If $$P(A) = 0.7$$, $$P(B) = 0.8$$, and $$P(A \cap B) = 0.65$$, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.7 + 0.8 - 0.65 = 0.85$$

Question 8

A machine produces 5% defective items. If 4 items are randomly selected, what is the probability exactly 1 is defective? (Use the binomial formula)

Accepted Answer

$$P(1) = \binom{4}{1} (0.05)^1$ (0.95)^3$

Question 9

A marketing campaign costs $$20,000. If successful (probability 0.4), profit is 80$$,000. If unsuccessful (probability 0.6), loss is $20,000. What is the expected net gain?

Accepted Answer

$$E = 0.4 	imes 60,000 + 0.6 	imes (-20,000) = 12,000$$

Question 10

A call center finds 30% of customers purchase an add-on. If 8 customers are contacted, what is the mean number of purchases?

Accepted Answer

$$\mu = np = 8 	imes 0.3 = 2.4$$

Question 11

Salaries are normally distributed with mean $$\60$$,000$$ and standard deviation $$\$$8,000. $$What percent of employees earn more than $$\72$$,000$?

Accepted Answer

About $$6.7\%$$

Question 12

For a normal distribution, what is the z-score corresponding to the 90th percentile?

Accepted Answer

$$z \approx 1.28$$

Question 13

A website averages 5 server errors per hour. What is the probability of more than 3 errors in an hour? (Poisson distribution)

Accepted Answer

$$P(X \u003e 3) = 1 - \sum_{x=0}^{3} \frac{e$$^{-5}$$ 5^x}{x!}$$

Question 14

Which chart is best for visualizing the relationship between two quantitative variables?

Accepted Answer

Scatter plot

Question 15

Which of the following is a property of the binomial distribution?

Accepted Answer

Fixed number of trials, two outcomes, constant probability

Question 16

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

Accepted Answer

$$0.5 	imes 0.4 = 0.2$$

Question 17

Which of the following best describes the coefficient of variation (CV)?

Accepted Answer

It standardizes risk by dividing standard deviation by the mean

Question 18

A correlation coefficient of $$-0.85$$ indicates:

Accepted Answer

A strong negative linear relationship

Question 19

Which Excel function would you use to find the x-value for a given probability in a normal distribution?

Accepted Answer

=NORM.INV()

Business Statistics Exam Study Guide: Step-by-Step Guidance

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