About 98% of the population.
Also normally distributed.
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.
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
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.
99.6% for
68.2%
The Z test.
The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.
True.
No, but the approximation is better for normally distributed variables.
Also normally distributed.
A particular fruit's weights are normally distributed, with a mean of 760 grams and a standard deviation of 15 grams. If you pick one fruit at random, what is the probability that it will weigh between 722 grams and 746 grams-----A particular fruit's weights are normally distributed, with a mean of 567 grams and a standard deviation of 25 grams.
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.
square (25/36) = 5/6 = .833
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.