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The standard deviation (SD) is a measure of spread so small sd = small spread. So the above is true for any distribution, not just the Normal.

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11y ago

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Test scores have a mean of 100 and a standard diviation of 20 what is the relative frequency of scores under 120?

Approx 84%.


How do you find normal distribution of z-scores?

z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.


What percentage of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution?

99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.


What role do z-scores play in the transformation of data from multiple distributions to the standard normal distribution?

None.z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.


What percent of the scores in a normal distribution will fall within one standard deviation?

It is 68.3%


In a standard normal distribution about percent of the scores fall above a z-score of 3.00?

0.13


Why does a researcher want to go from a normal distribution to a standard normal distribution?

A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.


How many of scores will be within 1 standard deviation of the population mean?

Assuming a normal distribution 68 % of the data samples will be with 1 standard deviation of the mean.


How much is 84 percentile equals mean plus 1 standard deviation or mean plus 1.4 standard deviation. Can you give me reference also please?

The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.


How would you characterize the distribution of scores in a normal distribution?

They are said to be Normally distributed.


Why does a researcher want to go from a normal distribution to a standard normal distributio?

A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.


What role do z scores play in this transformation of data from multiple distributions to standard normal distribution?

Z-scores standardize data from various distributions by transforming individual data points into a common scale based on their mean and standard deviation. This process involves subtracting the mean from each data point and dividing by the standard deviation, resulting in a distribution with a mean of 0 and a standard deviation of 1. This transformation enables comparisons across different datasets by converting them to the standard normal distribution, facilitating statistical analysis and interpretation.