Q: A factory has a 15% defect rate. If a customer buys 4 items, what is the probability that at least one item is defective?

$$P(\text{at least one defective}) = 1 - (0.85)^4$

Q: In a pre-employment drug screening, 45 out of 50 drug users test positive. What is the probability that a drug user tests positive?

$$P(\text{positive} | \text{uses drugs}) = \frac{45}{50} = 0.9$$

Q: Which formula is used to calculate the probability of event A or event B occurring, when the events are not mutually exclusive?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Q: A medical test for a disease has a true positive rate of 80% and a false positive rate of 10%. If the disease prevalence is 1%, what is the probability that a person who tests positive actually has the disease?

$$P(\text{disease} | \text{positive}) = \frac{0.008}{0.107} \approx 0.0748$$

Q: If a data set has a mean of $$50$$ and a standard deviation of $$8$$, what range of values would you expect to contain approximately 95% of the data according to the range rule of thumb?

$$50 \pm 2 \times 8 = 34 \text{ to } 66$$

Question 1

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

Accepted Answer

A parameter describes a characteristic of a population, while a statistic describes a characteristic of a sample.

Question 2

A researcher wants to study the average height of all students at a university. She randomly selects 100 students and measures their heights. What is the population in this study?

Accepted Answer

All students at the university.

Question 3

Which level of measurement is represented by the following data: 'Freshman', 'Sophomore', 'Junior', 'Senior'?

Accepted Answer

Ordinal

Question 4

A frequency distribution table is constructed for a set of exam scores. If the lower class limit of the first class is 50 and the class width is 10, what is the lower class limit of the third class?

Accepted Answer

$$70$$

Question 5

Which of the following graphs is most appropriate for displaying the distribution of categorical data such as favorite ice cream flavors?

Accepted Answer

Pie Chart

Question 6

A histogram of exam scores shows a longer tail on the right side. How is the distribution described?

Accepted Answer

Positively skewed

Question 7

Given the data set: $$10, 15, 20, 25, 30$$, what is the midrange?

Accepted Answer

$$20$$

Question 8

Which measure of center is most resistant to outliers?

Accepted Answer

Median

Question 9

A boxplot is constructed for a data set. The interquartile range (IQR) is $$12. $$What is the threshold for identifying outliers?

Accepted Answer

$$1.5 	imes 12 = 18$$

Question 10

If the mean wait time for a ride is $$30$$ minutes and the standard deviation is $$5$$ minutes, what is the z-score for a wait time of $$45$$ minutes?

Accepted Answer

$$z = \frac{45 - 30}{5} = 3$$

Question 11

A factory has a 15% defect rate. If a customer buys 4 items, what is the probability that at least one item is defective?

Accepted Answer

$$P(	ext{at least one defective}) = 1 - (0.85)^4$

Question 12

In a pre-employment drug screening, 45 out of 50 drug users test positive. What is the probability that a drug user tests positive?

Accepted Answer

$$P(	ext{positive} | 	ext{uses drugs}) = \frac{45}{50} = 0.9$$

Question 13

Which sampling method is most likely to produce a biased sample?

Accepted Answer

Convenience sampling

Question 14

A password consists of 4 digits, each from 0 to 9. How many possible passwords are there?

Accepted Answer

$$10^4 = 10$$,000$$

Question 15

Which formula is used to calculate the probability of event A or event B occurring, when the events are not mutually exclusive?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 16

A medical test for a disease has a true positive rate of 80% and a false positive rate of 10%. If the disease prevalence is 1%, what is the probability that a person who tests positive actually has the disease?

Accepted Answer

$$P(	ext{disease} | 	ext{positive}) = \frac{0.008}{0.107} \approx 0.0748$$

Question 17

Which of the following is an example of discrete data?

Accepted Answer

The number of students in a classroom.

Question 18

If a data set has a mean of $$50$$ and a standard deviation of $$8$$, what range of values would you expect to contain approximately 95% of the data according to the range rule of thumb?

Accepted Answer

$$50 \pm 2 	imes 8 = 34 	ext{ to } 66$$

Question 19

How many ways can a committee of 3 people be chosen from a group of 10?

Accepted Answer

$$\binom{10}{3} = 120$$

Foundations of Statistics: Concepts, Data, and Probability

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