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

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

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

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

Q: A quality control manager inspects 20 light bulbs from a large shipment. Each bulb has a 5% chance of being defective, independent of the others. What is the expected number of defective bulbs in the sample?

$$\mu = np = 20 \times 0.05 = 1$$

Q: If $$P(A) = 0.3$$ and $$P(B|A) = 0.5$$, what is $$P(A \text{ and } B)$$?

$$P(A \text{ and } B) = P(A) \times P(B|A) = 0.3 \times 0.5 = 0.15$$

Q: A company finds that 60% of its employees work the day shift and 1% of day-shift employees are absent on a given day. 40% work the night shift and 2% of night-shift employees are absent. What is the probability that a randomly selected employee is absent?

$$P(\text{absent}) = (0.6)(0.01) + (0.4)(0.02) = 0.014$$

Question 1

A university wants to estimate the average GPA of its students. They randomly select 100 students from a list of all enrolled students and calculate the mean GPA. Which of the following best describes the sampling method used?

Accepted Answer

Simple random sampling

Question 2

A researcher is interested in the effect of a new fertilizer on plant growth. She randomly assigns half of her plants to receive the new fertilizer and the other half to receive no fertilizer. She does not know which plants receive which treatment, and neither do the assistants measuring the plant heights. What type of experimental design is this?

Accepted Answer

Double-blind experiment

Question 3

Suppose $$P(A) = 0.4$$, $$P(B) = 0.5$$, 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 4

A pharmaceutical company wants to test a new drug. They divide participants into two groups: one receives the drug, the other receives a placebo. Participants are grouped by age before random assignment. What is this design called?

Accepted Answer

Randomized block design

Question 5

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 6

A survey asks all employees at a company about their job satisfaction. This is an example of:

Accepted Answer

Census

Question 7

A study finds that people who eat more vegetables tend to have lower cholesterol. However, people who exercise more also tend to eat more vegetables. What is 'exercise' in this context?

Accepted Answer

A lurking variable

Question 8

A random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.1$$, $$P(X=4)=?$$ What is the value of $$P(X=4)$$?

Accepted Answer

$$1 - (0.2 + 0.5 + 0.1) = 0.2$$

Question 9

A quality control manager inspects 20 light bulbs from a large shipment. Each bulb has a 5% chance of being defective, independent of the others. What is the expected number of defective bulbs in the sample?

Accepted Answer

$$\mu = np = 20 	imes 0.05 = 1$$

Question 10

A hospital wants to estimate the average wait time in its emergency room. They divide patients into three groups based on severity (mild, moderate, severe) and randomly sample from each group. This is an example of:

Accepted Answer

Stratified random sampling

Question 11

Suppose the probability that a randomly selected person has type O blood is $$0.45. If $$two people are selected independently, what is the probability that both have type O blood?

Accepted Answer

$$0.45 	imes 0.45 = 0.2025$$

Question 12

A sample of 100 batteries has a mean life of 120 hours and a standard deviation of 15 hours. What is the standard deviation of the sample mean?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{15}{\sqrt{100}} = 1.5$$

Question 13

A researcher wants to know if a new teaching method improves test scores. She randomly assigns students to either the new method or the traditional method and compares their final exam scores. What is the response variable?

Accepted Answer

Final exam score

Question 14

A random phenomenon has two possible outcomes: success with probability $$p$$ and failure with probability $$1-p. If $$the experiment is repeated $$n$$ times independently, which distribution models the number of successes?

Accepted Answer

Binomial distribution

Question 15

A study collects data on smoking habits and lung cancer rates by reviewing medical records from the past 20 years. What type of study is this?

Accepted Answer

Retrospective observational study

Question 16

If $$P(A) = 0.3$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B|A) = 0.3 	imes 0.5 = 0.15$$

Question 17

A company finds that 60% of its employees work the day shift and 1% of day-shift employees are absent on a given day. 40% work the night shift and 2% of night-shift employees are absent. What is the probability that a randomly selected employee is absent?

Accepted Answer

$$P(	ext{absent}) = (0.6)(0.01) + (0.4)(0.02) = 0.014$$

Question 18

A sample statistic is:

Accepted Answer

A value calculated from sample data, used to estimate a population parameter

Question 19

Which of the following is NOT a requirement for a binomial distribution?

Accepted Answer

The probability of success changes from trial to trial

Stat 101 Exam 2 Study Guide: Chapters 6–15 (Contingency Tables, Sampling, Probability, Binomial, and Sampling Distributions)

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