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| Section | Objectives |
|---|---|
| Probability | - Probability rules
|
| Regression and Correlation | - Relationship analysis
|
| Probability Distributions | - Discrete distributions
|
| Statistical Inference | - Hypothesis testing
|
| Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 82
Dataset: 3, 6, 9. Median?
Answer: D
Explanation:
The median is the middle value of a data set after the values are placed in ascending order. The dataset is 3, 6,
9, which is already ordered from least to greatest. Since there are three observations, the median is the second value, because one value lies below it and one value lies above it. Therefore, the median is 6. The median is a measure of center and is especially useful when data may be skewed or contain outliers because it depends on position rather than the magnitude of every value. The mean for this dataset is also 6, since (3 + 6 + 9) ÷ 3 =
6, but the question specifically asks for the median. Options B and C are not values in the dataset, and option D is the minimum value, not the middle. Study Guide references/topics: median, ordered data, measures of central tendency, descriptive statistics.
NEW QUESTION # 83
Z-score = ?
Answer: B
Explanation:
A z-score standardizes a raw value by expressing its distance from the mean in standard deviation units. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. The numerator x # # measures how far the value is from the mean. Dividing by # converts that distance into standard deviation units. A positive z-score means the value is above the mean, a negative z-score means the value is below the mean, and z = 0 means the value equals the mean. Option B divides the raw value by the mean and does not measure standardized distance. Option C reverses the ratio incorrectly. Option D gives only the raw deviation and fails to standardize by the standard deviation. Z-scores are central in normal distribution calculations and comparisons across different scales. Study Guide references/topics: z-score, standardization, mean, standard deviation.
NEW QUESTION # 84
Two dice rolled, probability of both even = ?
Answer: A
Explanation:
A standard six-sided die has three even outcomes: 2, 4, and 6. Thus, the probability that one die lands on an even number is 3/6 = 1/2. When two dice are rolled, the outcomes are independent because the result of one die does not affect the other. Therefore, the probability that both dice are even is 1/2 × 1/2 = 1/4.
Equivalently, there are 36 ordered outcomes for two dice. The even-even outcomes are formed from 3 even choices on the first die and 3 even choices on the second die, giving 3 × 3 = 9 favorable outcomes. Then 9/36 simplifies to 1/4. Option B gives the probability of one die being even, not both. Options C and D do not match the count or multiplication rule. Study Guide references/topics: independent events, dice probability, multiplication rule, sample space.
NEW QUESTION # 85
Probability of drawing red card from deck = ?
Answer: C
Explanation:
A standard deck has 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red, while clubs and spades are black. Each suit has 13 cards, so the number of red cards is 13 +
13 = 26. The probability of drawing a red card is therefore the number of favorable outcomes divided by the total number of outcomes: 26/52. This simplifies to 1/2. Option B, 1/4, would describe the probability of drawing one specific suit, such as hearts only. Option C, 1/13, would describe one specific rank in the deck, such as a particular value across suits. Option D does not correspond to the card structure of a standard deck.
Since exactly half the deck is red, the correct probability is 26/52 = 1/2. Study Guide references/topics: card probability, favorable outcomes, sample space, theoretical probability.
NEW QUESTION # 86
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?
Answer: A
Explanation:
The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.
NEW QUESTION # 87
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