Questions & Answers
Browse all 25 questions from the
Advanced Statistics and Probability study set below.
Each question shows the correct answer — select a study format above to practice interactively.
1
In a normal distribution, what percentage of the data falls within three standard deviations of the mean?
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A
68.2%
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B
95.4%
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C
99.7%
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D
99.9%
2
Which measure of central tendency is most sensitive to extreme outliers in a dataset?
-
A
Median
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B
Mode
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C
Arithmetic Mean
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D
Geometric Mean
3
What is the probability of drawing two consecutive aces from a standard 52-card deck without replacement?
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A
1/13
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B
1/221
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C
4/663
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D
1/169
4
Which statistical term describes the 'spread' of a dataset, calculated as the square root of the variance?
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A
Interquartile Range
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B
Standard Deviation
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C
Coefficient of Variation
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D
Mean Absolute Deviation
5
In probability theory, what does the 'Law of Large Numbers' state happens as the number of trials increases?
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A
The experimental probability approaches the theoretical probability
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B
The variance becomes zero
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C
The distribution becomes skewed
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D
The sample size becomes irrelevant
6
What is the sum of the probabilities of all mutually exclusive and exhaustive outcomes in a sample space?
7
Which value represents the median of a dataset?
-
A
The average of all values
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B
The 50th percentile
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C
The most frequent value
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D
The difference between maximum and minimum
8
In a binomial distribution, what does 'n' represent?
-
A
Number of successes
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B
Probability of failure
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C
Number of independent trials
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D
The expected value
9
What is the degree of freedom for a sample variance calculated from a dataset of size n?
10
Which statistical test is used to determine if there is a significant difference between the means of two groups?
-
A
Chi-squared test
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B
T-test
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C
ANOVA
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D
Regression analysis
11
What is the range of a probability value?
-
A
-1 to 1
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B
0 to 1
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C
0 to 100
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D
Negative infinity to infinity
12
Which term describes the tail of a distribution being longer or fatter on one side?
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A
Kurtosis
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B
Skewness
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C
Standardization
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D
Correlation
13
If two events A and B are independent, what is the formula for the probability of both occurring?
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A
P(A) + P(B)
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B
P(A) * P(B)
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C
P(A) / P(B)
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D
P(A) - P(B)
14
What does the 'p-value' represent in hypothesis testing?
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A
The probability of the null hypothesis being true
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B
The significance level
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C
The probability of observing results as extreme as the data given the null hypothesis
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D
The correlation coefficient
15
Which graph displays the frequency distribution of a continuous variable using bins?
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A
Pie chart
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B
Histogram
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C
Scatter plot
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D
Line graph
16
What is the relationship between correlation and causation?
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A
Correlation implies causation
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B
Causation implies correlation
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C
Correlation does not imply causation
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D
They are the same concept
17
In a standard normal distribution (Z-distribution), what is the mean?
18
Which statistical measure identifies the middle 50% of the data?
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A
Range
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B
Standard Deviation
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C
Interquartile Range
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D
Variance
19
What is the probability of rolling a sum of 7 with two fair six-sided dice?
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A
1/6
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B
1/12
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C
1/36
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D
1/7
20
What is the complement of event A if the probability of A is 0.35?
21
Which coefficient measures the strength and direction of a linear relationship between two variables?
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A
R-squared
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B
Pearson correlation coefficient
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C
Z-score
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D
T-statistic
22
How many outcomes are possible when flipping a fair coin 4 times?
23
What is the variance of a constant value?
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A
0
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B
1
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C
The constant itself
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D
Infinite
24
What does the 'Central Limit Theorem' imply about the distribution of sample means?
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A
It is always uniform
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B
It is always binomial
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C
It approaches a normal distribution as sample size increases
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D
It is always the same as the population distribution
25
Which distribution describes the probability of a given number of events occurring in a fixed interval of time?
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A
Normal
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B
Poisson
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C
Binomial
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D
Geometric
