2024-03-14T01:11:37+03:00[Europe/Moscow] en true <p>What are 3 features of a normal distribution?</p>, <p>When is a distribution treated as a normal distribution?</p>, <p>What is 1 con about the normal distribution?</p>, <p>What is a Z score (or, standard deviation value)?</p>, <p>What are Z scores 'converting'?</p>, <p>What is the mean when it's expressed as a Z score?</p>, <p>What is the standard normal distribution? </p>, <p>Approximately what % of a standard normal distribution is within 2 S.D units of the mean? (1 above and 1 below?)</p>, <p>Approximately what % of a standard normal distribution is within 4 S.D units of the mean? (2 above and 2 below?)</p>, <p>Approximately what % of a standard normal distribution is within 6 S.D units of the mean? (3 above and 3 below?)</p>, <p>What is the "68%-95%-99.7% Rule"? </p>, <p>What is a Z table (standard normal table)?</p>, <p>If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % of students will score above 105?</p><p>- What are the steps to solve this?</p>, <p>If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % will score between 97 and 103?</p><p>- What are the steps to solve this?</p>, <p>If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, how high would one need to score to be in the 95th percentile?</p><p>- What are the steps to solve this?</p>, <p>Z scores use probability of what % of the area under the curve falls <strong>below or to the left </strong>of a given Z score, how do you find out % of the area under the curve <u>falls to the right</u> of a Z score?</p> flashcards
Normal Distribution & Z Scores

Normal Distribution & Z Scores

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  • What are 3 features of a normal distribution?

    1. Bell-shaped

    2. Symmetrical

    3. The mode, median, and mean are equal

  • When is a distribution treated as a normal distribution?

    If it's roughly symmetrical

  • What is 1 con about the normal distribution?

    Most distributions are theoretical, as a true normal distribution is rare to find in nature

  • What is a Z score (or, standard deviation value)?

    The number of standard deviations a given raw score falls above or below the mean

  • What are Z scores 'converting'?

    Raw data (cases/single observations) into standard deviation units, where 1 'S.D unit' constitutes 1 step away from the mean of a distribution

  • What is the mean when it's expressed as a Z score?

    Always 0, since it's 0 'steps' away from itself

  • What is the standard normal distribution?

    A normal distribution represented as Z scores where mean = 0 and standard deviation = 1

  • Approximately what % of a standard normal distribution is within 2 S.D units of the mean? (1 above and 1 below?)

    68%

  • Approximately what % of a standard normal distribution is within 4 S.D units of the mean? (2 above and 2 below?)

    95%

  • Approximately what % of a standard normal distribution is within 6 S.D units of the mean? (3 above and 3 below?)

    99.7%

  • What is the "68%-95%-99.7% Rule"?

    A normally distributed data set has a constant relationship with it's standard deviation. such that, a given S.D above/below the mean will always account for the same proportion (%) of data under the curve

  • What is a Z table (standard normal table)?

    A table that, if given a Z score, can determine the probability (% or chance) of a given raw score falling under a specific area of a curve, or, for calculating the area under a curve between any two points

  • If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % of students will score above 105?

    - What are the steps to solve this?

    30.8%

    1. Use the raw score to find the Z score using the correct formula

    2. Find the corresponding value on the z-table

    3. SUBTRACT that value from 1.00 since Z scores always represent less than (<)/to the left and we're interested in greater than (>)/to the right

  • If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % will score between 97 and 103?

    - What are the steps to solve this?

    23.5%

    1. use BOTH raw scores to find their Z scores using the correct formula

    2. Find their corresponding values on the z-table

    3. subtract from EACH OTHER to find the area under the curve between the two scores

  • If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, how high would one need to score to be in the 95th percentile?

    - What are the steps to solve this?

    116.5

    1. Find the corresponding value on the z-table that best matches the 95th percentile (95%)

    2. Find it's corresponding Z score

    3. Use the raw score formula to convert the Z score back into a raw score

  • Z scores use probability of what % of the area under the curve falls below or to the left of a given Z score, how do you find out % of the area under the curve falls to the right of a Z score?

    Subtract the Z score from 1.00 since the distribution has to be 100% = 1.00. If a Z score represents what's to the left, and you subtract it from 1.00, anything left over must be what's to the right of the Z score