Q: A bag contains 5 red balls and 7 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

$$\frac{5}{12} \times \frac{4}{11}$$

Q: If two events A and B are independent, which of the following is true?

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

Question 1

Suppose a researcher calculates the linear correlation coefficient $$r$$ between hours studied and exam scores for a group of students and finds $$r = 0.85. $$Which of the following best describes this relationship?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 2

Given the least squares regression line $$\hat{y} = 2.5 + 0.8x$$, what is the predicted value of $$y$$ when $$x = 10$$?

Accepted Answer

$$\hat{y} = 10.5$$

Question 3

A study finds that the coefficient of determination $$R^2$$ for the relationship between exercise frequency and cholesterol level is $$0.64. $$What does this mean?

Accepted Answer

64% of the variation in cholesterol level can be explained by exercise frequency.

Question 4

Which of the following is the correct formula for the slope $$b_1 of $$the least squares regression line?

Accepted Answer

$$b_1$$ = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x}$$)^2$$}$$

Question 5

A contingency table is used to:

Accepted Answer

Display the frequency distribution of variables and analyze the association between categorical variables.

Question 6

If the probability of event A is 0.3 and the probability of event B is 0.5, and A and B are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$P(A \cup B) = 0.8$$

Question 7

A bag contains 5 red balls and 7 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

Accepted Answer

$$\frac{5}{12} 	imes \frac{4}{11}$$

Question 8

Which of the following is the correct formula for the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$p_i$$?

Accepted Answer

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

Question 9

An insurance company models the number of claims per customer per year as a binomial random variable with $$n = 5$$ and $$p = 0.1. $$What is the probability that a customer files exactly 2 claims in a year?

Accepted Answer

$$P(X=2) = \binom{5}{2} (0.1)^2$ (0.9)^3$

Question 10

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

The mean, median, and mode are all equal.

Question 11

A standard normal variable $$Z$$ has mean 0 and standard deviation 1. What is $$P(Z \u003c 1.96)$$?

Accepted Answer

Approximately 0.975

Question 12

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

Accepted Answer

$$z = 2$$

Question 13

A hospital records the number of patients who recover from a certain treatment. If the probability of recovery is 0.7 and 8 patients are treated, what is the expected number of recoveries?

Accepted Answer

$$E(X) = 8 	imes 0.7 = 5.6$$

Question 14

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is defined only for discrete values.

Question 15

A fair coin is tossed 10 times. What is the probability of getting exactly 6 heads?

Accepted Answer

$$P(X=6) = \binom{10}{6} (0.5)^6$ (0.5)^4$

Question 16

If two events A and B are independent, which of the following is true?

Accepted Answer

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

Question 17

A student scores 1.5 standard deviations above the mean on a standardized test. If the mean is 500 and the standard deviation is 100, what is the student's score?

Accepted Answer

$$650$$

Question 18

Which of the following best describes the use of the standard normal table?

Accepted Answer

It provides the area under the standard normal curve to the left of a given $$z-$$score.

Question 19

A medical test for a disease has a 95% chance of correctly identifying a diseased patient (sensitivity) and a 90% chance of correctly identifying a healthy patient (specificity). If 1% of the population has the disease, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$P(	ext{positive}) = 0.01 	imes 0.95 + 0.99 	imes 0.10$$

Question 20

If a fair die is rolled twice, what is the probability that the sum is 7?

Accepted Answer

$$\frac{6}{36}$$

Statistics Study Guide: Regression, Probability, and the Normal Distribution

Study Guide - Practice Questions

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