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| Section | Objectives |
|---|---|
| Topic 1: Regression and Correlation | - Relationship analysis
|
| Topic 2: Statistical Inference | - Estimation
|
| Topic 3: Descriptive Statistics | - Data visualization
|
| Topic 4: Probability Distributions | - Continuous distributions
|
| Topic 5: Probability | - Fundamental probability concepts
|
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NEW QUESTION # 110
Rare event count per interval modeled by:
Answer: B
Explanation:
The Poisson distribution is used to model the number of events occurring in a fixed interval of time, space, area, or volume when the events occur independently at a constant average rate. It is especially common for rare event counts, such as calls arriving at a help desk per hour, accidents at an intersection per month, defects per production batch, or website errors per day. The defining parameter of the Poisson distribution is #, the average number of events per interval. A binomial distribution instead models the number of successes in a fixed number of independent trials with a constant probability of success. A normal distribution models continuous, bell-shaped measurements. A uniform distribution assigns equal probability across outcomes or intervals. Because the prompt specifically says "rare event count per interval," the technical match is the Poisson distribution. Study Guide references/topics: Poisson distribution, event counts, rate parameter #, discrete probability distributions.
NEW QUESTION # 111
The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
Assuming a normal distribution, which two values encompass 95% of the data?
Answer: C
Explanation:
For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 112
In a standard normal distribution, z-score for the mean = ?
Answer: D
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 # 113
Probability of rolling an even number on a six-sided die?
Answer: A
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 # 114
Standard deviation squared = ?
Answer: D
Explanation:
Variance and standard deviation are directly connected measures of spread. Variance is calculated by averaging squared deviations from the mean, while standard deviation is the square root of variance.
Therefore, reversing that relationship, standard deviation squared equals variance. Symbolically, if the standard deviation is s, then the sample variance is s². This relationship matters because variance is expressed in squared units, while standard deviation is expressed in the original units of measurement. For example, if test-score standard deviation is 4 points, the variance is 4² = 16 square points. The mean and median are measures of center, not squared spread. The standard error measures the variability of a sample statistic, usually the sample mean, across repeated samples. The correct answer is variance because it is the squared form of standard deviation. Study Guide references/topics: standard deviation, variance, measures of spread, descriptive statistics.
NEW QUESTION # 115
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