C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
1. 33. Which of the following best describes the purpose of the line of best fit in a scatterplot?
- A) To connect all plotted data points exactly
- B) To show the average of the x-values only
- C) To estimate the trend or relationship between two variables
- D) To determine the mode of a data set
Explanation
The line of best fit, or regression line, provides a visual summary of the relationship between two variables. It shows the general direction of data points—upward, downward, or neutral—and is used to predict one variable’s value based on the other. It does not connect each data point but instead minimizes overall distance from them.
2. 18. If P(A) = 0.4 and P(B) = 0.5 and A and B are independent, what is P(A and B)?
- A) 0.9
- B) 0.2
- C) 0.45
- D) 0.1
Explanation
For independent events, the probability of both occurring is found by multiplying their individual probabilities: P(A and B) = P(A) × P(B) = 0.4 × 0.5 = 0.2. This property applies only when the occurrence of one event does not affect the probability of the other.
3. 19. When constructing a boxplot, which measure identifies potential outliers?
- A) Mean
- B) Median
- C) Interquartile range
- D) Mode
Explanation
The interquartile range (IQR) is used to detect outliers in a boxplot. Values that lie more than 1.5 times the IQR above Q3 or below Q1 are considered potential outliers. This helps in identifying unusually high or low observations that may distort statistical analysis.
4. 93. Which of the following would cause the range of a data set to increase?
- A) Adding a value near the mean
- B) Removing an outlier
- C) Adding a new extreme value
- D) Reducing the largest number
Explanation
The range depends on the difference between the largest and smallest values. Adding a new extreme (either very high or low) value increases that difference, thereby increasing the range and overall variability in the data.
5. 5. When two variables show a consistent increase or decrease together, what type of correlation exists?
- A) Positive correlation
- B) Negative correlation
- C) No correlation
- D) Curvilinear correlation
Explanation
A positive correlation occurs when one variable increases as the other increases. This indicates a direct relationship between the two variables. For example, height and weight often show a positive correlation. The relationship is measured using the correlation coefficient (r), where values closer to +1 signify a strong positive relationship.
6. 65. If 8x = 64, what is the value of x?
- A) 6
- B) 7
- C) 8
- D) 9
Explanation
Divide both sides by 8 to isolate x: x = 64 ÷ 8 = 8. This demonstrates solving one-step algebraic equations, a foundational concept for applying algebra in statistical formulas and modeling.
7. 7. Which graphical display is most appropriate for showing the distribution of a single categorical variable?
- A) Histogram
- B) Pie chart
- C) Scatterplot
- D) Boxplot
Explanation
A pie chart effectively represents categorical data by dividing a circle into sectors that correspond to the proportion of each category. It provides an intuitive visual comparison of parts to a whole. In contrast, histograms and boxplots are used for quantitative data, while scatterplots show relationships between two variables.
8. 92. If a frequency table shows that most students score near the mean with few high and low values, which shape does the distribution likely have?
- A) Uniform
- B) Skewed left
- C) Skewed right
- D) Approximately normal
Explanation
When most data cluster around the mean with symmetrical tapering toward the extremes, the distribution is approximately normal. This bell-shaped curve is common in real-world data like test scores and biological measurements.
9. 20. Which of the following is an example of a categorical variable?
- A) Weight of newborns
- B) Number of books read in a month
- C) Type of vehicle owned
- D) Age of students
Explanation
A categorical variable represents qualitative data, describing categories or types rather than numerical values. “Type of vehicle owned” is categorical because it classifies data into groups such as sedan, SUV, or truck, without numerical measurement or order.
10. 74. Which of the following best describes conditional probability?
- A) The probability of one event occurring regardless of another
- B) The probability of one event given that another has already occurred
- C) The probability of all events happening together
- D) The probability that an event is impossible
Explanation
Conditional probability measures the likelihood of one event occurring when another is known to have occurred. It’s expressed as P(A|B), read “the probability of A given B.” It’s key to understanding dependent events in real-world contexts like testing and quality control.
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