C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
A frequency distribution shows that most data values are clustered on the left side with a long tail to the right. What is this distribution called?
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Symmetric
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Negatively skewed
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Positively skewed
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Uniform
Explanation
When a distribution has a long tail extending to the right, it is positively skewed. This means that most data values are smaller, but a few larger values pull the mean toward the higher end, creating asymmetry in the graph.
Which of the following is an example of a dependent event?
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Flipping a coin and rolling a die
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Drawing two cards from a deck without replacement
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Rolling two dice at the same time
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Spinning a spinner and tossing a coin
Explanation
Dependent events occur when the outcome of one affects the probability of the other. Drawing cards without replacement is dependent because removing one card changes the deck composition, altering the chance of drawing the next card.
A researcher finds that as study hours increase, test anxiety decreases. This is an example of:
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Positive correlation
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Negative correlation
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No correlation
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Spurious correlation
Explanation
A negative correlation means that as one variable increases, the other decreases. In this case, more study hours correspond to lower anxiety levels. The correlation coefficient (r) would have a negative value, indicating an inverse relationship between the two variables.
Which of the following values could represent a standard deviation?
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–5
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0
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–3
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–1
Explanation
Standard deviation measures data spread and is always zero or positive because it is derived from squared differences. A standard deviation of 0 indicates no variation; negative values are mathematically impossible.
The slope of a line in algebra represents:
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The y-intercept of the line
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The change in y for each unit change in x
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The midpoint between two points on the line
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The area under the curve
Explanation
The slope measures how steep a line is by showing the rate of change between two variables. It is calculated as rise over run, or Δy/Δx. A positive slope indicates an upward trend, while a negative slope indicates a downward trend between variables.
If a number is multiplied by 0, the result is always:
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1
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0
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Undefined
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The number itself
Explanation
Any number multiplied by zero equals zero. This fundamental property of multiplication reflects that zero represents the absence of quantity, so combining any number with nothing yields nothing. This property is often used in simplifying algebraic expressions.
If 40% of a class are left-handed and 60% are right-handed, what is the probability that a randomly selected student is right-handed?
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0.2
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0.4
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0.6
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0.8
Explanation
Probabilities express the likelihood of events and always range between 0 and 1. Given that 60% of the students are right-handed, the probability of randomly selecting one who is right-handed equals 0.6, which represents 60 out of every 100 students.
A company records employee ages and monthly income. Which type of data relationship is being examined?
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Categorical vs. categorical
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Quantitative vs. quantitative
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Categorical vs. quantitative
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Nominal vs. ordinal
Explanation
Both age and monthly income are quantitative variables. Analyzing their relationship helps identify numerical patterns, such as whether older employees earn more, through methods like correlation or regression.
Which of the following is true for a correlation coefficient (r)?
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It can exceed 1
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It ranges between –1 and +1
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It cannot be negative
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It always equals 0 for unrelated variables
Explanation
The correlation coefficient (r) quantifies the direction and strength of a linear relationship between two variables. It ranges from –1 (perfect negative) to +1 (perfect positive). A value of 0 indicates no linear relationship.
Which of the following best describes a population in a statistical study?
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A subset of individuals selected for analysis
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The entire group of individuals or items being studied
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A group chosen by random sampling from a population
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A group selected based on convenience
Explanation
A population includes all individuals, items, or data points relevant to a particular study. When researchers want to understand characteristics of an entire group—such as all students in a university—they refer to that as the population. A sample, on the other hand, is only a portion of the population used to make inferences.
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