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What requirements are necessary for a normal probability distribution to be a standard normal probability?
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
For a normal distribution what z-score value separates the lowest 10 percent of the scores from the rest of the distribution?
-1.28
What proportion of a normal distribution corresponds to z-scores greater than plus 1.04?
To find the proportion of a normal distribution corresponding to z-scores greater than +1.04, you can use the standard normal distribution table or a calculator. The area to the left of z = 1.04 is approximately 0.8508. Therefore, the proportion of the distribution that corresponds to z-scores greater than +1.04 is 1 - 0.8508, which is approximately 0.1492, or 14.92%.
When the normal curve is plotted according to standard deviation units each having a value of 1.00 what is it called?
When the normal curve is plotted using standard deviation units, each with a value of 1.00, it is referred to as the standard normal distribution. In this distribution, the mean is 0 and the standard deviation is 1, allowing for easy comparison of different data sets by transforming them into z-scores. The standard normal distribution is often represented by the symbol Z.
How are scores distributed if the mean is 100 and the standard deviation is 15?
If the mean score is 100 and the standard deviation is 15, the distribution of scores is likely to follow a normal distribution, also known as a bell curve. In this distribution, approximately 68% of scores fall within one standard deviation of the mean (between 85 and 115), about 95% fall within two standard deviations (between 70 and 130), and about 99.7% fall within three standard deviations (between 55 and 145). This pattern indicates that most scores cluster around the mean, with fewer scores appearing as you move away from the center.
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
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 requirements are necessary for a normal probability distribution to be a standard normal probability?
For a normal probability distribution to be considered a standard normal probability distribution, it must have a mean of 0 and a standard deviation of 1. This standardization allows for the use of z-scores, which represent the number of standard deviations a data point is from the mean. Any normal distribution can be transformed into a standard normal distribution through the process of standardization.
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.
For a normal distribution what z-score value separates the lowest 10 percent of the scores from the rest of the distribution?
-1.28
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.
Why in a normal distribution the distribution will be less spread out when the standard diviation of the raw scores is small?
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.
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.
z scores?
If a random variable X has a normal distribution with mean m and standard error s, then the z-score corresponding to the value X = x is (x - m)/s.
For a normal distribution find the z-scores values that separate the middle 60 percent of the distribution for the 40 percent in the tails?
The standard normal table tells us the area under a normal curve to the left of a number z. The tables usually give only the positive value since one can use symmetry to find the corresponding negative values. The middle 60 percent leaves 20 percent on either side. So we want the z scores that correspond to that 80 percentile which is .804. Therefore the values are are between z scores of -.804 and .804 * * * * * I make it -0.8416 to 0.8416
What proportion of a normal distribution corresponds to z-scores greater than plus 1.04?
To find the proportion of a normal distribution corresponding to z-scores greater than +1.04, you can use the standard normal distribution table or a calculator. The area to the left of z = 1.04 is approximately 0.8508. Therefore, the proportion of the distribution that corresponds to z-scores greater than +1.04 is 1 - 0.8508, which is approximately 0.1492, or 14.92%.
