Questions and Answers
All of the following characteristics are true about a normal distribution except:
A normal distribution has a mean equal to 5. What is the value of the median and mode in this distribution?
5
The area under a normal curve ranges from 0 to 1 and can never be negative. What type of statistics also has these same characteristics?
Probability
What term best describes behavior that falls within 2 SD of the mean in a normal distribution?
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The normal distribution is used to determine the probability of a certain outcome _____________ to all other outcomes.
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State the two steps for locating proportion under the normal curve:
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State two steps for locating scores in a distribution with a given probability:
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A probability distribution for binomial outcomes approximates the shape of what type of distribution?
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The larger the sample size, the more closely a binomial probability distribution will approximate a normal distribution.
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To use the normal approximation for the binomial distribution, np and nq must be equal to at least what value?
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What is a Z-score?
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What is a normal distribution?
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What are the eight characteristics of a normal distribution?
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In the standard normal distribution, the value of the mean is?
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In the standard normal distribution, the value of standard deviation is?
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What does the binomial distribution approximates to the normal distribution imply?
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Approximately 95% of scores in a normal distribution fall within?
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5% of scores fall?
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Study Notes
Characteristics of Normal Distribution
- Normal distributions have a symmetrical shape with the mean, median, and mode all aligning at the center.
- Tails of a normal distribution do not touch the x-axis at 3 standard deviations (SD) from the mean; this is a misconception.
- A normal distribution can have a mean of any value (positive or negative), and its variance can only be positive.
Relationship Between Mean, Median, and Mode
- In a normal distribution where the mean is 5, both the median and mode also equal 5.
Probability Characteristics
- The area under the normal curve always ranges from 0 to 1, reflecting total probability, similar to probability distributions.
Statistical Norms
- Behavior within 2 standard deviations of the mean is described as falling within statistical norms.
Unit Normal Table
- Z-scores are listed in Column A of the unit normal table.
- Column C shows the area from z-scores toward the tail.
- The area between a z-score and the mean is found in Column B.
Probability in Relation
- Normal distribution is used to determine the probability of an outcome in relation to all other outcomes.
Locating Proportions Under the Normal Curve
- First step: Transform a raw score (X) into a z-score.
- Second step: Locate the corresponding probability for that z-score in the unit normal table.
Locating Scores with Given Probability
- Step 1: Find the z-score associated with the desired proportion in the unit normal table.
- Step 2: Convert the z-score back into a raw score.
Binomial Outcomes
- A probability distribution for binomial outcomes approximates the shape of a normal distribution, especially with larger sample sizes.
Sample Size Impact
- A true statement: As sample size increases, the binomial probability distribution more closely approximates a normal distribution.
Conditions for Normal Approximation
- To utilize normal approximation for a binomial distribution, both np and nq must be at least 10.
Z-Score Definition
- A z-score indicates the value within a standard normal distribution, reflecting the distance of a value from its mean.
Normal Distribution Definition
- A theoretical distribution characterized by symmetrical data around the mean, as well as the median and mode.
Eight Characteristics of Normal Distribution
- Mathematically defined and theoretical in nature.
- Mean, median, and mode are at the 50th percentile.
- The standard deviation can be any positive value, and the total area under the curve equals 1.
- Tails are asymptotic, approaching but never touching the x-axis.
Standard Normal Distribution Values
- Mean in a standard normal distribution is always 0.
- Standard deviation in a standard normal distribution is always 1.
Approximation of Binomial to Normal Distribution
- The binomial distribution approximates a normal distribution as sample size increases.
Distribution of Scores
- Approximately 95% of scores fall within 2 standard deviations from the mean.
- Conversely, 5% of scores fall outside 2 standard deviations from the mean.
Studying That Suits You
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Description
This quiz focuses on the characteristics of normal distribution, testing your knowledge on its key features and properties. Each flashcard presents a statement regarding normal distribution, requiring you to identify which characteristic is false. Perfect for statistics students wanting to reinforce their understanding.
