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| Section | Objectives |
|---|---|
| Topic 1: Statistical Inference | - Estimation
|
| Topic 2: Probability | - Fundamental probability concepts
|
| Topic 3: Probability Distributions | - Continuous distributions
|
| Topic 4: Regression and Correlation | - Relationship analysis
|
| Topic 5: Descriptive Statistics | - Data summarization
|
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NEW QUESTION # 94
Sample mean = 60; point estimate of population mean = ?
Answer: B
Explanation:
A point estimate is a single sample statistic used to estimate an unknown population parameter. When estimating a population mean, the standard point estimate is the sample mean. In this question, the sample mean is given as 60. Therefore, the point estimate of the population mean is also 60. This does not mean the true population mean is guaranteed to equal 60; rather, 60 is the best single numerical estimate based on the available sample. Confidence intervals build on this point estimate by adding and subtracting a margin of error to reflect sampling uncertainty. Option B is incorrect because although the true population mean is unknown, the point estimate is known. Option C and option D do not correspond to the sample statistic provided. The logic is central to inferential statistics: use sample evidence to estimate population characteristics. Study Guide references/topics: sample mean, population mean, point estimation, inferential statistics.
NEW QUESTION # 95
Expected value of binomial X ~ B(10, 0.3) = ?
Answer: C
Explanation:
For a binomial random variable, the expected value is E(X) = np, where n is the number of trials and p is the probability of success on each trial. In this problem, X ~ B(10, 0.3), so n = 10 and p = 0.3. Substituting into the formula gives E(X) = 10 × 0.3 = 3. This means that across many repetitions of the same binomial experiment, the average number of successes would be 3. Option B, 7, would correspond to the expected number of failures if the failure probability is 0.7. Option C gives only the number of trials, not the expected successes. Option D gives only the success probability, not the expected count. The expected value combines both trial count and success probability. Study Guide references/topics: binomial distribution, expected value, success probability, discrete random variables.
NEW QUESTION # 96
Probability of rolling sum = 2 on 2 dice = ?
Answer: C
Explanation:
When two standard six-sided dice are rolled, there are 6 × 6 = 36 equally likely ordered outcomes. To get a sum of 2, the only possible ordered pair is (1, 1). No other pair of die faces can produce a total of 2 because 1 is the smallest value on each die. Therefore, there is 1 favorable outcome out of 36 total outcomes, giving a probability of 1/36. Option B, 1/6, is the probability of one specific result on a single die, not a two-dice sum.
Option C, 2/36, would require two favorable ordered pairs, but only one exists. Option D, 1/12, is also too large because it corresponds to 3 outcomes out of 36. The key is to count ordered outcomes in the full two- dice sample space. Study Guide references/topics: dice probability, sample space, favorable outcomes, theoretical probability.
NEW QUESTION # 97
Conditional probability formula:
Answer: A
Explanation:
Conditional probability measures the probability that event A occurs given that event B has already occurred.
The formula is P(A|B) = P(A and B)/P(B), assuming P(B) is greater than zero. The denominator P(B) restricts the sample space to cases where B occurs, and the numerator P(A and B) counts cases where both A and B occur within that restricted space. Option B is incorrect because it divides P(A) by P(B) without requiring overlap between A and B. Option C reverses the conditioning and would relate to P(B|A) only if the numerator were P(A and B). Option D applies to independent events when finding P(A and B), not to conditional probability in general. The vertical bar in P(A|B) is read as "given," and it signals that the denominator should be the probability of the given event. Study Guide references/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 98
Determine z in the equation:
1/(6z) = 2/9
Answer: C
Explanation:
The equation 1/(6z) = 2/9 is a proportion because it sets two fractions equal to each other. To solve it, use cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the denominator of the first fraction by the numerator of the second fraction: 1 × 9 = 2 × 6z. This gives 9 = 12z. To isolate z, divide both sides by 12: z = 9/12. This fraction can also be simplified to 3/4, but the answer choices list the unsimplified equivalent form 9/12. The other options do not satisfy the original equation. For example, if z = 2/54, then 6z is very small and the left side becomes much larger than 2/9. If z =
12/9 or 18/2, the denominator becomes too large, making the left side too small. References/topics from the Study Guide: proportions, solving equations, cross multiplication, equivalent fractions.
NEW QUESTION # 99
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