Q: A bag contains 4 red balls and 6 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

$$\frac{4}{10} \times \frac{3}{9}$$

Q: A fair die is rolled twice. What is the probability of getting a 6 on both rolls?

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

Question 1

Which of the following best describes the meaning of the linear correlation coefficient $$r in $$the context of a medical study examining the relationship between hours of exercise per week and cholesterol levels?

Accepted Answer

It indicates the strength and direction of the linear relationship between hours of exercise and cholesterol levels.

Question 2

Given the least squares regression line $$\hat{y} = 2.5x + 10$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 20$$

Question 3

A researcher finds $$r = -0.85$$ between hours spent studying and number of errors on a test. What does this value of $$r$$ indicate?

Accepted Answer

There is a strong negative linear relationship between hours spent studying and number of errors.

Question 4

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

Accepted Answer

$$\mu = \sum x \cdot P(x)$$

Question 5

A car insurance company uses the expected value to set premiums. If the probability of a claim is $$0.02$$ and the average claim amount is $$\5$$,000$, what is the expected payout per customer?

Accepted Answer

$$\100$

Question 6

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

Accepted Answer

The distribution is skewed to the right.

Question 7

If a student scores 1.5 standard deviations above the mean on a standardized test, what is their $$z-$$score?

Accepted Answer

$$z = 1.5$$

Question 8

Using the binomial probability formula, what is the probability of getting exactly 3 heads in 5 flips of a fair coin?

Accepted Answer

$$P(X=3) = \binom{5}{3} (0.5)^3$ (0.5)^2$

Question 9

Which rule should be used to find the probability of either event $$A or $$event $$B$$ occurring, if $$A$$ and $$B$$ are mutually exclusive?

Accepted Answer

Addition Rule: $$P(A \cup B) = P(A) + P(B)$$

Question 10

A bag contains 4 red balls and 6 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

Accepted Answer

$$\frac{4}{10} 	imes \frac{3}{9}$$

Question 11

Which of the following best describes the coefficient of determination $$R^2 in a $$regression analysis of advertising spending and sales revenue?

Accepted Answer

It measures the proportion of variation in sales revenue explained by advertising spending.

Question 12

A student is asked to count the number of ways to arrange the letters in the word 'STATISTICS'. Which counting technique should be used?

Accepted Answer

Permutations of non-distinct items

Question 13

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 14

A fair die is rolled twice. What is the probability of getting a 6 on both rolls?

Accepted Answer

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

Question 15

Which of the following is the correct formula for the area under the standard normal curve between $$z = -1$$ and $$z = 1$$?

Accepted Answer

$$P(-1 \u003c Z \u003c 1) = \Phi(1) - \Phi(-1)$$

Question 16

A factory produces light bulbs with a 2% defect rate. If a box contains 20 bulbs, what is the probability that exactly one bulb is defective? (Use the binomial formula)

Accepted Answer

$$P(X=1) = \binom{20}{1} (0.02)^1$ (0.98$$)^{19}$$

Question 17

Which of the following is an example of using the multiplication rule in probability?

Accepted Answer

Finding the probability of drawing two aces in a row from a deck without replacement.

Question 18

A student randomly selects 3 books from a shelf of 10. How many different combinations of books can be selected?

Accepted Answer

$$\binom{10}{3}$$

Question 19

If the correlation coefficient $$r$$ between two variables is $$0$$, what does this imply about their relationship?

Accepted Answer

There is no linear relationship between the variables.

Key Concepts in Statistics: Regression, Probability, and the Normal Distribution

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