Q: A card is drawn from a standard deck. What is the probability that it is either a heart or a king?

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

Q: A fair die is rolled twice. What is the probability that both rolls show a 6?

$$\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$$

Question 1

A researcher wants to estimate the average cholesterol level of adults in a city. She randomly selects 200 adults and calculates the average cholesterol level from their blood samples. Which of the following best describes the average cholesterol level calculated from the 200 adults?

Accepted Answer

It is a statistic because it is calculated from a sample.

Question 2

Which of the following scenarios best describes an experiment rather than an observational study?

Accepted Answer

Researchers assign one group of patients a new drug and another group a placebo, then compare recovery rates.

Question 3

A cumulative frequency distribution is most useful for which of the following purposes?

Accepted Answer

To show the total number of observations below each class boundary.

Question 4

Which of the following is a sign that a histogram may be deceptive?

Accepted Answer

The horizontal axis uses unequal class widths.

Question 5

Given the data set: 2, 4, 4, 6, 8, what is the midrange?

Accepted Answer

$$\frac{2+8}{2} = 5$$

Question 6

A sample of exam scores has a mean of 70 and a standard deviation of 8. What is the z-score for a student who scored 86?

Accepted Answer

$$z = \frac{86-70}{8} = 2$$

Question 7

Which of the following best describes the empirical rule for a normal distribution?

Accepted Answer

All of the above.

Question 8

A boxplot is constructed from a data set. Which of the following statements is true?

Accepted Answer

The box represents the interquartile range (IQR).

Question 9

If the probability of an event A is 0.3, what is the probability of the complement of A?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 10

A card is drawn from a standard deck. What is the probability that it is either a heart or a king?

Accepted Answer

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

Question 11

A hospital administrator wants to select a sample of patients such that every patient has an equal chance of being chosen. Which sampling method should be used?

Accepted Answer

Simple random sampling

Question 12

Which of the following is the correct formula for the variance $$s^2 of a $$sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 13

A company wants to know if a new training program improves employee productivity. They randomly assign half of the employees to the new program and the other half to the old program, then compare results. What type of study is this?

Accepted Answer

Experiment

Question 14

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

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 15

How many different ways can 5 books be arranged on a shelf?

Accepted Answer

$$5! = 120$$

Question 16

A stemplot is most useful for which of the following?

Accepted Answer

Displaying the distribution of a small set of quantitative data.

Question 17

A fair die is rolled twice. What is the probability that both rolls show a 6?

Accepted Answer

$$\frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$$

Question 18

Which of the following is NOT a property of probabilities?

Accepted Answer

The probability of any event can be negative.

Question 19

A researcher wants to estimate the average income of households in a large city. She divides the city into neighborhoods, randomly selects 5 neighborhoods, and surveys all households in those neighborhoods. What sampling method is this?

Accepted Answer

Cluster sampling

Question 20

If a data set has a mean of 50 and a standard deviation of 5, what range of values would you expect to contain approximately 95% of the data according to the empirical rule?

Accepted Answer

$$50 \pm 2 	imes 5 = 40 	ext{ to } 60$$

Statistics Fundamentals: Key Concepts and Methods

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