Q: Given the probability model for a dice game: win $$70 with probability $$\frac{2}{6}$$, win 30 $$with probability $$\frac{8}{36}$$, and win $$0 with probability $$\frac{16}{36}$, what is the expected value of the amount won?

$$E(X) = 70 \times \frac{2}{6} + 30 \times \frac{8}{36} + 0 \times \frac{16}{36}$$

Q: Given the probability model: win $$70 with probability $$\frac{2}{6}$$, win 30 $$with probability $$\frac{4}{6}$$, what is the expected value of the amount won?

$$E(X) = 70 \times \frac{2}{6} + 30 \times \frac{4}{6}$$

Question 1

Refer to the three histograms of test scores for Class 1, Class 2, and Class 3. Which class has the smallest interquartile range (IQR), and why?

Accepted Answer

Class 3, because the data is symmetric and concentrated around the center.

Question 2

Given the scatterplot that forms a perfect diagonal straight line from bottom left to top right, what is the most likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r = 1$$

Question 3

Which of the following scatterplots best represents a correlation coefficient close to zero?

Accepted Answer

A plot with points randomly scattered with no pattern.

Question 4

Given the scatterplot that forms a downward sloping straight line, what is the sign of the correlation coefficient $$r$$?

Accepted Answer

Negative

Question 5

A scatterplot shows a U-shaped (parabolic) pattern. What is the value of the correlation coefficient $$r$$ for this data?

Accepted Answer

$$r is $$close to 0

Question 6

Given the table of heights (in cm) and reading scores, if the heights were converted to inches, what would happen to the correlation coefficient $$r$$?

Accepted Answer

It would remain the same.

Question 7

Refer to the boxplots of case prices for Vineyards A, B, and C. Which vineyard produces the most expensive wine, and why?

Accepted Answer

Vineyard B, because it has the highest maximum value.

Question 8

Given the probability model for a dice game: win $$70 with probability $$\frac{2}{6}$$, win 30 $$with probability $$\frac{8}{36}$$, and win $$0 with probability $$\frac{16}{36}$, what is the expected value of the amount won?

Accepted Answer

$$E(X) = 70 	imes \frac{2}{6} + 30 	imes \frac{8}{36} + 0 	imes \frac{16}{36}$$

Question 9

In the scatterplot with labeled points A, B, C, and D, which point is most likely to be influential in determining the regression line?

Accepted Answer

Point B

Question 10

Given the probability model: win $$100 with probability $$\frac{4}{36}$$, win 70 $$with probability $$\frac{8}{36}$$, win $$30 with probability $$\frac{8}{36}$$, and win 0 $$with probability $$\frac{16}{36}$$, what is the sum of all probabilities?

Accepted Answer

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

Question 11

Which formula correctly represents the calculation of the correlation coefficient $$r$$ using standardized values?

Accepted Answer

$$r = \frac{\sum z_x z_y}{n-1}$$

Question 12

Which formula correctly represents the calculation of the correlation coefficient $$r$$ using sample standard deviations?

Accepted Answer

$$r = \frac{S_{xy}}{S_x S_y}$$

Question 13

Given the probability model: win $$100 with probability $$\frac{4}{36}$$, win 70 $$with probability $$\frac{2}{36}$$, win $$30 with probability $$\frac{2}{36}$$, and win 0 $$with probability $$\frac{16}{36}$$, what is the probability of winning at least $70?

Accepted Answer

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

Question 14

Refer to the Z-table provided. What is the probability that a standard normal variable $$Z is $$less than 1.28?

Accepted Answer

0.8997

Question 15

Refer to the Z-table provided. What is the probability that a standard normal variable $$Z is $$greater than -1.00?

Accepted Answer

0.8413

Question 16

Given the probability model: win $$70 with probability $$\frac{2}{6}$$, win 30 $$with probability $$\frac{4}{6}$$, what is the expected value of the amount won?

Accepted Answer

$$E(X) = 70 	imes \frac{2}{6} + 30 	imes \frac{4}{6}$$

Question 17

The scatterplot of world population (in millions) versus year shows a concave upward curve. For which range of years is a linear model most appropriate?

Accepted Answer

0 through 1000 and 1400 through 1800

Question 18

Given the table of means and standard deviations for variables X and Y, what is the mean and standard deviation of the variable $$0.8Y$$?

Accepted Answer

$$\mu = 24, \sigma = 6.4$$

Statistics Practice Exam Guidance – Visuals, Probability, and Data Analysis

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