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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Predictions and limitations of regression - Correlation coefficient and interpretation - Simple linear regression models - Interpreting slope, intercept, and R-squared |
| Topic 2: Probability Concepts | 20% | - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions |
| Topic 3: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots |
| Topic 4: Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Sampling methods and bias - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions |
| Topic 5: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
>> Applied-Probability-and-Statistics最新考古題 <<
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問題 #70
A teacher plots the test scores of a class using the box plot.
What is true about the test scores?
答案:D
解題說明:
A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.
問題 #71
Probability of rolling an even number on a six-sided die?
答案:C
解題說明:
A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The even outcomes are 2, 4, and
6. That gives 3 favorable outcomes out of 6 total outcomes. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2. Option A, 1/3, would correspond to 2 favorable outcomes out of 6, which is not correct here. Option C, 1/6, is the probability of rolling one specific number, such as only a 2.
Option D, 2/3, would require 4 favorable outcomes out of 6. Since exactly half of the die faces are even and half are odd, the probability of rolling an even number is one-half. Study Guide references/topics: theoretical probability, equally likely outcomes, sample space, favorable outcomes.
問題 #72
What is the mode of this dataset: 3, 5, 7, 7, 10?
答案:C
解題說明:
The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode.
This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.
問題 #73
Mean of Poisson # = 5 = ?
答案:C
解題說明:
For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.
問題 #74
Z-score negative #
答案:B
解題說明:
A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.
問題 #75
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