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Q: The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the minimum weight of the middle 95 percent of the players?

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The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.

68.2%

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.

True.

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.

67% as it's +/- one standard deviation from the mean

If a normally distributed random variable X has mean m and standard deviation s, then z = (X - m)/s

It is 0.37, approx.

If a variable X, is distributed Normally with mean m and standard deviation s thenZ = (X - m)/s has a standard normal distribution.

Standard deviation is a way to describe how the data is distributed around the Arithmatic Mean. It is not a simple formula to calculate, as shown in the links.

about 25

For normally distributed data. One standard deviation (1σ)Percentage within this confidence interval68.2689492% (68.3% )Percentage outside this confidence interval31.7310508% (31.7% )Ratio outside this confidence interval1 / 3.1514871 (1 / 3.15)

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