Q: Which formula is used to calculate the probability of two independent events $$A$$ and $$B$$ both occurring?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Given a scatterplot showing the relationship between hours studied and exam scores, which of the following statements best describes a positive correlation?

Accepted Answer

As hours studied increase, exam scores tend to increase.

Question 2

Suppose the correlation coefficient $$r$$ between two variables is $$-0.85. $$What does this indicate about the relationship?

Accepted Answer

There is a strong negative linear relationship.

Question 3

A researcher finds $$r = 0.02$$ between daily coffee consumption and hours of sleep. What is the best interpretation?

Accepted Answer

There is essentially no linear relationship.

Question 4

Which formula is used to calculate the slope $$b of $$the least squares regression line?

Accepted Answer

$$b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2$}$$

Question 5

If the regression equation for predicting income from years of education is $$\hat{y} = 20 + 3x$$, what is the predicted income for someone with 10 years of education?

Accepted Answer

$$\50$

Question 6

Which of the following is NOT a valid use of a regression line?

Accepted Answer

Extrapolating far beyond the observed data.

Question 7

Which formula is used to calculate the probability of two independent events $$A$$ and $$B$$ both occurring?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 8

A bag contains 5 red, 3 blue, and 2 green marbles. If you randomly select one marble, what is the probability it is not blue?

Accepted Answer

$$0.7$$

Question 9

Which of the following best describes the difference between theoretical and empirical probability?

Accepted Answer

Theoretical probability is based on mathematical reasoning; empirical is based on observed data.

Question 10

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 11

A fair die is rolled. What is the probability of rolling an even number OR a number greater than 4?

Accepted Answer

$$\frac{4}{6}$$

Question 12

Which formula is used to calculate the expected value $$E(X) of a $$discrete random variable $$X$$?

Accepted Answer

$$E(X) = \sum x_i P(x_i)$$

Question 13

A binomial experiment consists of 8 trials with probability of success $$p = 0.25. $$What is the expected number of successes?

Accepted Answer

$$2$$

Question 14

Which of the following is a property of a normal distribution?

Accepted Answer

It is symmetric about the mean.

Question 15

If a random variable $$X is $$normally distributed with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the $$z-$$score for $$X = 130$$?

Accepted Answer

$$z = 2$$

Question 16

A student scores in the 90th percentile on a standardized test. What does this mean?

Accepted Answer

The student scored higher than 90% of all test-takers.

Question 17

Which formula is used to convert a raw score $$x to a$$ $$z-$$score in a normal distribution?

Accepted Answer

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

Question 18

A hospital records the number of patients admitted each day. Which type of random variable best describes this data?

Accepted Answer

Discrete random variable

Question 19

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

Accepted Answer

Probability of success changes from trial to trial.

Question 20

A company wants to know if their new product launch is successful. They define success as selling at least 100 units in a day. Which probability distribution is most appropriate to model the number of successful days in a month?

Accepted Answer

Binomial distribution

Statistics Exam 2 Study Guide: Correlation, Probability, and Distributions

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