Q: Which of the following is the formula for the coefficient of variation (CV) for a sample?

$$CV = \frac{s}{\bar{x}} \times 100\%$$

Q: A fair die is rolled 60 times. What is the expected number of times a '6' will appear?

$$\mu = np = 60 \times \frac{1}{6} = 10$$

Q: If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \text{ and } B) = 0.2$$, what is $$P(A \text{ or } B)$$?

$$P(A \text{ or } B) = 0.4 + 0.5 - 0.2 = 0.7$$

Question 1

A company receives an average of 12 customer complaints per week. What is the probability that they receive exactly 15 complaints in a given week? (Use the Poisson distribution.)

Accepted Answer

$$P(x=15) = \frac{e$$^{-12}$$ \cdot 12$$^{15}$$}{15!}$$

Question 2

Which of the following is the correct formula for the z-score of a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 3

A survey asks 100 randomly selected people if they prefer coffee or tea. Which distribution should you use to model the probability of exactly 60 people preferring coffee?

Accepted Answer

Binomial distribution

Question 4

A machine produces bolts with lengths that are normally distributed with mean $$\mu = 5 cm $$and standard deviation $$\sigma = 0.2 cm. $$What is the probability that a randomly selected bolt is between 4.8 cm and 5.2 cm?

Accepted Answer

Approximately 68% (using the empirical rule)

Question 5

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter describes a population; a statistic describes a sample.

Question 6

If a process is described as 'the time between arrivals of buses at a stop,' which probability distribution is most appropriate?

Accepted Answer

Exponential distribution

Question 7

A quality control inspector samples 10 items from a batch of 50 without replacement. Which distribution should be used to find the probability that exactly 3 are defective?

Accepted Answer

Hypergeometric distribution

Question 8

Which of the following is the formula for the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100\%$$

Question 9

A random variable $$X is $$uniformly distributed between $$a = 10$$ and $$b = 30. $$What is the probability that $$X is $$between 15 and 25?

Accepted Answer

$$P(15 \leq X \leq 25) = \frac{25 - 15}{30 - 10} = 0.5$$

Question 10

Which of the following statements is TRUE about the mean and median in a right-skewed distribution?

Accepted Answer

The mean is greater than the median.

Question 11

A fair die is rolled 60 times. What is the expected number of times a '6' will appear?

Accepted Answer

$$\mu = np = 60 	imes \frac{1}{6} = 10$$

Question 12

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.4 + 0.5 - 0.2 = 0.7$$

Question 13

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution?

Accepted Answer

The probability $$p$$ must be close to 0 or 1.

Question 14

A business analyst wants to compare the consistency of two machines producing bolts. Machine A has $$s = 0.5 mm $$and $$\bar{x} = 10 mm. $$Machine B has $$s = 0.3 mm $$and $$\bar{x} = 6 mm. $$Which machine is more consistent?

Accepted Answer

Machine B, because it has a lower coefficient of variation.

Question 15

If the probability that a part is defective is $$0.02$$, what is the probability that at least one part is defective in a sample of 10 parts?

Accepted Answer

$$1 - (0.98$$)^{10}$$

Question 16

Which of the following is the formula for the probability of exactly $$x$$ successes in $$n$$ binomial trials with probability $$p of $$success?

Accepted Answer

$$P(x) = \binom{n}{x} p^x (1-p$$)^{n-x}$$

Question 17

A dataset contains the following values: 2, 4, 4, 4, 5, 5, 7, 9. What is the median?

Accepted Answer

4.5

Question 18

Which of the following is TRUE about mutually exclusive events?

Accepted Answer

They cannot both happen at the same time.

Question 19

If $$\lambda = 3$$ per hour for an exponential distribution, what is the mean time between events?

Accepted Answer

$$\mu = \frac{1}{\lambda} = \frac{1}{3}$$ hours

Business Statistics Midterm Study Guide: Chapters 1–6

Guida di studio - Domande di pratica

Study guide - Flashcard