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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Sampling methods and bias - Observational studies vs experiments - Hypothesis testing framework and interpretation |
| Topic 2: Probability Concepts | 20% | - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions - Conditional probability and Venn diagrams |
| Topic 3: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
| Topic 4: Descriptive Statistics | 25% | - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation |
| Topic 5: Correlation & Regression | 20% | - Predictions and limitations of regression - Correlation coefficient and interpretation - Simple linear regression models - Interpreting slope, intercept, and R-squared |
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NEW QUESTION # 105
In a standard normal distribution, z-score for the mean = ?
Answer: C
Explanation:
A z-score measures how many standard deviations a value is above or below the mean. The formula is z = (x
# #) / #, where x is the observed value, # is the mean, and # is the standard deviation. If the observed value equals the mean, then x = #. Substituting into the formula gives z = (# # #) / # = 0 / # = 0. Therefore, the z- score corresponding to the mean is always 0 in any normal distribution, including the standard normal distribution. In the standard normal distribution specifically, the mean is 0 and the standard deviation is 1, so the mean lies exactly at z = 0. A z-score of 1 would indicate one standard deviation above the mean, and #1 would indicate one standard deviation below the mean. Study Guide references/topics: standard normal distribution, z-scores, mean, standard deviation.
NEW QUESTION # 106
Probability of rolling an even number on a six-sided die?
Answer: D
Explanation:
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.
NEW QUESTION # 107
Probability of drawing king or queen from deck = ?
Answer: C
Explanation:
A standard deck contains 52 cards. There are 4 kings and 4 queens, one of each rank in each suit. The event is drawing a king or a queen. Since a single card cannot be both a king and a queen, these two events are mutually exclusive. Therefore, the number of favorable outcomes is 4 + 4 = 8. The probability is favorable outcomes divided by total outcomes: 8/52. This fraction can be simplified to 2/13, but the answer choice provides the unsimplified correct form. Option B, 4/52, counts only kings or only queens, not both. Option C,
1/13, is equivalent to 4/52 and again represents one rank only. Option D, 1/26, is too small and does not match the count of favorable cards. The word "or" signals that both qualifying ranks should be included. Study Guide references/topics: card probability, mutually exclusive events, addition rule, sample space.
NEW QUESTION # 108
Random variable X = number of heads in 4 coin flips #
Answer: C
Explanation:
The random variable X counts the number of heads obtained in 4 coin flips. Since it is a count, it can take only specific whole-number values: 0, 1, 2, 3, or 4. It cannot take fractional values such as 2.5 heads. A random variable with countable possible outcomes is classified as discrete. This situation also fits a binomial framework because there is a fixed number of independent trials, each trial has two outcomes, and the probability of heads remains constant for a fair coin. A continuous random variable, by contrast, can take any value over an interval, such as time, weight, or height. The number of heads is not measured on a continuum; it is counted. Therefore, the correct classification is discrete. Study Guide references/topics: discrete random variables, binomial setting, coin-flip outcomes, probability distributions.
NEW QUESTION # 109
Probability of exactly 1 head in 2 coin flips = ?
Answer: D
Explanation:
Two coin flips produce four equally likely ordered outcomes: HH, HT, TH, and TT. Exactly one head occurs in two of these outcomes: HT and TH. Therefore, the probability is 2 favorable outcomes out of 4 total outcomes, or 2/4 = 1/2. This can also be computed using the binomial model. There are n = 2 independent trials, success probability p = 1/2, and exactly one success is required. The binomial calculation is C(2,1)(1/2)