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| Section | Objectives |
|---|---|
| Probability Distributions | - Discrete distributions
|
| Descriptive Statistics | - Data summarization
|
| Statistical Inference | - Estimation
|
| Probability | - Fundamental probability concepts
|
| Regression and Correlation | - Relationship analysis
|
>> Applied-Probability-and-Statistics Relevant Questions <<
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NEW QUESTION # 146
Sample mean = 40, SD = 8, n = 16. Standard error = ?
Answer: D
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.
NEW QUESTION # 147
In a city's public transportation system, the distribution of commuters by mode of transport is as follows: 40% use buses, 25% use trains, 20% use bicycles, 10% walk, and 5% use other means of transportation.
What is the probability that a randomly selected commuter uses either a bus or a train?
Answer: C
Explanation:
The event is that a randomly selected commuter uses either a bus or a train. These categories are mutually exclusive because one commuter is classified under one primary transportation mode in the given distribution.
For mutually exclusive events, the probability of "A or B" is found by adding the individual probabilities. The probability of using a bus is 40%, and the probability of using a train is 25%. Therefore, P(bus or train) = 40%
+ 25% = 65%. The bicycle, walking, and other transportation categories are not included because the question restricts the event to bus or train only. Option B, 45%, would incorrectly combine bus with the 5% "other" category or otherwise omit part of the train group. Option C is too low, and option A is unrelated to the stated categories. References/topics from the Study Guide: probability, mutually exclusive events, addition rule, percentage distributions.
NEW QUESTION # 148
Histogram vs bar chart:
Answer: C
NEW QUESTION # 149
Ten teachers each had a jar of jelly beans. The jars had this number of jelly beans in each respective jar: 50,
60, 80, 80, 100, 100, 100, 120, 120, and 140.
What is the mean of these data?
Answer: A
Explanation:
The mean is the arithmetic average of a quantitative data set. To calculate it, add all observed values and divide by the number of observations. The jelly bean counts are 50, 60, 80, 80, 100, 100, 100, 120, 120, and
140. Their sum is 950. There are 10 jars, so the mean is 950 ÷ 10 = 95. This means the average number of jelly beans per jar is 95. Option A, 100, may seem plausible because 100 appears frequently and is near the center of the data, but frequency alone determines the mode, not the mean. Option C, 80, is one of the repeated values but not the average. Option B, 120, is too high because several observations fall well below
120. The mean uses every value in the data set, including the low values 50 and 60 and the high value 140.
References/topics from the Study Guide: mean, measures of center, quantitative data, arithmetic average.
NEW QUESTION # 150
Poisson mean = 4. Probability of exactly 2 events?