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Q: What percentage of normally distributed scores lie under the normal curve?

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2

True or False, One major advantage of transforming X values into z-scores is that the z-scores always form a normal distribution

190-195. I got those scores in 2nd grade but they should be average in 3rd grade.

The transformation always creates a normal shaped distribution.

You call it a bell shaped curved. It may or may not be Gaussian (Normal).

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They are said to be Normally distributed.

...normally distributed.

Normally distributed.

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

X = 50 => Z = (50 - 70)/12 = -20/12 = -1.33 So prob(X < 50) = Prob(Z < -1.33...) = 0.091

2

The heights or masses of adult males, or of adult females. IQ scores (whatever they measure).

The answer depends on what SAT tests. In the UK the mean is 100 and the SD approx 15 - the scores are truncated at 100 +/- 44.

Anything that is normally distributed has certain properties. One is that the bulk of scores will be near the mean and the farther from the mean you are, the less common the score. Specifically, about 68% of anything that is normally distributed falls within one standard deviation of the mean. That means that 68% of IQ scores fall between 85 and 115 (the mean being 100 and standard deviation being 15) AND 68% of adult male heights fall between 65 and 75 inches (the mean being 70 and I am estimating a standard deviation of 5). Basically, even though the means and standard deviations change, something that is normally distributed will keep these probabilities (relative to the mean and standard deviation). By standardizing these numbers (changing the mean to 0 and the standard deviation to 1) we can use one table to find the probabilities for anything that is normally distributed.

about 25

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

About 98% of the population.

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