Characteristics of Normal Distribution Flashcards
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Questions and Answers

All of the following characteristics are true about a normal distribution except:

  • The shape of the normal distribution is symmetrical.
  • The mean can be any positive or negative number.
  • The variance can be any positive number.
  • Tails of a normal distribution touch the x-axis at the 3 SD from the mean. (correct)

    • 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?

    <p>Statistical Norms</p> Signup and view all the answers

    The normal distribution is used to determine the probability of a certain outcome _____________ to all other outcomes.

    <p>in relation or relative</p> Signup and view all the answers

    State the two steps for locating proportion under the normal curve:

    <p>Step 1: transforms a raw score (X) into a z-score; Step 2: locate the corresponding probability for the z-score in the unit normal table</p> Signup and view all the answers

    State two steps for locating scores in a distribution with a given probability:

    <p>Step 1: locate the z-score associated with a given proportion in the unit normal table; Step 2: transform the z-score into a raw score</p> Signup and view all the answers

    A probability distribution for binomial outcomes approximates the shape of what type of distribution?

    <p>A normal distribution</p> Signup and view all the answers

    The larger the sample size, the more closely a binomial probability distribution will approximate a normal distribution.

    <p>True</p> Signup and view all the answers

    To use the normal approximation for the binomial distribution, np and nq must be equal to at least what value?

    <p>10</p> Signup and view all the answers

    What is a Z-score?

    <p>Value of a standard normal distribution.</p> Signup and view all the answers

    What is a normal distribution?

    <p>Theoretical distribution which includes data that are symmetrically distributed around the mean.</p> Signup and view all the answers

    What are the eight characteristics of a normal distribution?

    <ol> <li>The normal distribution is mathematically defined. 2. Normal distribution is theoretical. 3. The mean, median, mode are all located at the 50th percentile. 4. Normal distribution is symmetrical. 5. The mean can equal any value. 6. Standard deviation can equal any positive value. 7. Total area under the normal curve is equal to 1. 8. Tails of a normal distribution are asymptotic.</li> </ol> Signup and view all the answers

    In the standard normal distribution, the value of the mean is?

    <p>0</p> Signup and view all the answers

    In the standard normal distribution, the value of standard deviation is?

    <p>1</p> Signup and view all the answers

    What does the binomial distribution approximates to the normal distribution imply?

    <p>When the sample size is large, the binomial distribution more closely approximates the normal distribution.</p> Signup and view all the answers

    Approximately 95% of scores in a normal distribution fall within?

    <p>2 standard deviations of the mean</p> Signup and view all the answers

    5% of scores fall?

    <p>outside 2 SD of the mean</p> Signup and view all the answers

    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.

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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.

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