Question 1

Which of the following best describes the difference between descriptive and inferential statistics in a business context?

Accepted Answer

Descriptive statistics summarize and present data, while inferential statistics use sample data to make predictions or estimates about a population.

Question 2

A company collects the following data on the number of products sold each day: 12, 15, 14, 10, 19. What is the sample mean?

Accepted Answer

$$ \frac{12 + 15 + 14 + 10 + 19}{5} = 14 $$

Question 3

Which formula would you use to calculate the sample variance $$s^2$$ for a data set?

Accepted Answer

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

Question 4

A distribution of exam scores is skewed to the right. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 5

If a student’s test score is at the 90th percentile, what does this mean?

Accepted Answer

The student scored higher than 90% of the students.

Question 6

Which of the following is NOT a requirement for the probability distribution of a discrete random variable $$x$$?

Accepted Answer

$$ \sum p(x) = 0 $$

Question 7

A business wants to know the probability of exactly 3 successes in 5 independent trials, where the probability of success on each trial is 0.4. Which formula should be used?

Accepted Answer

$$ p(x) = \binom{5}{3} (0.4)^3$ (0.6)^2$ $$

Question 8

Which of the following best describes a continuous random variable?

Accepted Answer

A variable that can take on any value within an interval.

Question 9

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

Accepted Answer

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

Question 10

Which of the following statements about the Empirical Rule is correct?

Accepted Answer

About 68% of the data falls within one standard deviation of the mean.

Question 11

A company uses Excel’s BINOM.DIST(2, 5, 0.3, FALSE) function. What does this compute?

Accepted Answer

The probability of exactly 2 successes in 5 trials with probability 0.3.

Question 12

If the sample variance $$s^2 is 16$$, what is the sample standard deviation $$s$$?

Accepted Answer

$$ s = \sqrt{16} = 4 $$

Question 13

Which of the following is a property of probabilities for sample points in a sample space?

Accepted Answer

The sum of the probabilities of all sample points is 1.

Question 14

A random variable $$X$$ has the following probability distribution: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is the expected value $$E(X)$$?

Accepted Answer

$$ E(X) = 0 	imes 0.2 + 1 	imes 0.5 + 2 	imes 0.3 = 1.1 $$

Question 15

Which of the following is NOT a characteristic of a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 16

A business analyst wants to estimate the population mean using a sample. Which of the following statistics is used as the estimate?

Accepted Answer

The sample mean $$\overline{x}$$

Question 17

If a data set has a minimum value of 10 and a maximum value of 50, what is the range?

Accepted Answer

$$ 50 - 10 = 40 $$

Question 18

Which of the following best describes the rule of complements in probability?

Accepted Answer

The sum of the probabilities of complementary events equals 1.

Question 19

A company wants to know the probability of getting at most 3 successes in 10 trials with probability 0.2. Which Excel function should they use?

Accepted Answer

BINOM.DIST(3, 10, 0.2, TRUE)

Business Statistics Study Guide: Chapters 1–4 (MAT 137)

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