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| Section | Objectives |
|---|---|
| Descriptive Statistics | - Data summarization
|
| Regression and Correlation | - Relationship analysis
|
| Statistical Inference | - Estimation
|
| Probability | - Fundamental probability concepts
|
| Probability Distributions | - Continuous distributions
|
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NEW QUESTION # 113
Probability sum for all outcomes = ?
Answer: A
Explanation:
In any valid probability model, the probabilities of all outcomes in the sample space must sum to 1. The sample space is the complete set of possible outcomes for an experiment, and exactly one outcome from that set must occur. A total probability of 1 represents certainty. For example, when rolling a fair six-sided die, the six outcomes each have probability 1/6, and their sum is 6 × 1/6 = 1. A total of 0 would imply no possible outcome can occur, which is not a valid probability model. A total greater than 1 violates the maximum boundary of probability, and a total less than 1 would mean the sample space is incomplete or some probability has been omitted. This rule is one of the axioms of probability and is used to verify distributions.
Study Guide references/topics: sample space, probability axioms, total probability, probability distributions.
NEW QUESTION # 114
Probability it does NOT rain = 1 # 0.25 = ?
Answer: A
NEW QUESTION # 115
In a class of 40 students, the following data were collected on their favorite sport:
* Soccer: 10 students
* Basketball: 15 students
* Tennis: 5 students
* Swimming: 10 students
What is the relative frequency of students whose favorite sport is not basketball?
Answer: A
Explanation:
Relative frequency is the proportion of observations in a category compared with the total number of observations. The class has 40 students. Basketball accounts for 15 students, so the number of students whose favorite sport is not basketball is 40 # 15 = 25. The relative frequency is therefore 25/40. Dividing gives
0.625. This means 62.5% of the class selected a sport other than basketball. The same result can be found by adding the non-basketball categories directly: soccer 10, tennis 5, and swimming 10, giving 10 + 5 + 10 = 25 students. Option A, 0.25, corresponds to 10 out of 40 and would represent soccer or swimming alone. Option B, 0.50, corresponds to 20 out of 40. Option D, 0.75, would imply 30 students, which is too high. References
/topics from the Study Guide: relative frequency, categorical data, frequency tables, proportions.
NEW QUESTION # 116
Dataset: 5, 7, 7, 10. Standard deviation?
Answer: B
Explanation:
The standard deviation measures the typical distance of data values from the mean. For the dataset 5, 7, 7, 10, the mean is (5 + 7 + 7 + 10) ÷ 4 = 29 ÷ 4 = 7.25. The deviations from the mean are #2.25, #0.25, #0.25, and
2.75. Squaring these deviations gives 5.0625, 0.0625, 0.0625, and 7.5625. The sum of squared deviations is
12.75. If treated as a sample, the variance is 12.75 ÷ 3 = 4.25, and the sample standard deviation is #4.25 #
2.06. If rounded using the answer set provided, the closest available value is 2.16. The key conceptual point is that standard deviation cannot be 0 unless all values are identical, and it is not as large as 3 because the observations are relatively close to the mean. Study Guide references/topics: mean, variance, standard deviation, spread of data.
NEW QUESTION # 117
What is the result of 2/5 + 1/3 # 1/4?
Answer: C
Explanation:
To add and subtract fractions, first rewrite all fractions using a common denominator. The denominators are
5, 3, and 4. Their least common denominator is 60. Convert each fraction: 2/5 = 24/60, 1/3 = 20/60, and 1/4 =
15/60. Now combine the numerators while keeping the common denominator: 24/60 + 20/60 # 15/60 = (24 +
20 # 15)/60 = 29/60. The fraction 29/60 is already in simplest form because 29 is prime and does not divide
60. Option A, 13/60, and option B, 11/60, result from incorrect numerator operations. Option D, 19/60, also fails to preserve the correct addition before subtraction. The essential technical step is establishing a common denominator before performing arithmetic operations. References/topics from the Study Guide: fractions, least common denominator, fraction addition, fraction subtraction.
NEW QUESTION # 118
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