Properties of Normal Dist.

Properties of the Normal Distribution

The normal distribution describes many natural processes, like people's heights, many manufacturing and social processes, as well as chance processes. When people say the bell curve they are referring to she shape of the normal distribution. The curve at the right shows the distribution of men's heights in a population with an average height of 69 inches (175 cm) and a standard deviation of 3 inches (7.5 cm). The curve shows that most men have a height near the average with fewer men having extreme heights. The area under the curve is proportional to the number of men whose height we would expect to find in a given height interval.
The lower normal curve shows the heights of a sample of 18 men. Each dot represents one person's height. The heights of most men cluster near the mean height. The pattern of most heights near the average and fewer away from the average gives the distribution of heights its familiar bell curve shape.

Why is there no vertical scale? The horizontal scale is a number line. Recall that the probability of a hitting a number, say 65, exactly on a number line is zero! This is because there are an infinite number of values in the neighborhood of 65. So we can't make a vertical bar at 65. But we can say that there are heights between 64.5 and 65.5 and that about 5% of the area under the curve lies between those two values. When you use the normal curve, look at the x-axis values and the area under the curve. Disregard the height (the y-axis values) of the curve. There is more on this topic in the empirical rule section. Also the normal curve is smooth. The small squiggles on the curve you see on your computer screen are from plotting in pixels.
The histograms discussed in previous sections are all discrete distributions, in which the height of the bar measures frequency. Note that since the bars are all equal width, height is actually a measure of area. Thus the area concept holds for discrete distributions as well.

The normal distribution is a continuous distribution because the x-axis values are not broken into specific hit or miss values.

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The normal distribution describes many natural processes, like people's heights, many manufacturing and social processes, as well as chance processes. When people say the bell curve they are referring to she shape of the normal distribution. The curve at the right shows the distribution of men's heights in a population with an average height of 69 inches (175 cm) and a standard deviation of 3 inches (7.5 cm). The curve shows that most men have a height near the average with fewer men having extreme heights. The area under the curve is proportional to the number of men whose height we would expect to find in a given height interval. The lower normal curve shows the heights of a sample of 18 men. Each dot represents one person's height. The heights of most men cluster near the mean height. The pattern of most heights near the average and fewer away from the average gives the distribution of heights its familiar bell curve shape.

	Why is there no vertical scale? The horizontal scale is a number line. Recall that the probability of a hitting a number, say 65, exactly on a number line is zero! This is because there are an infinite number of values in the neighborhood of 65. So we can't make a vertical bar at 65. But we can say that there are heights between 64.5 and 65.5 and that about 5% of the area under the curve lies between those two values. When you use the normal curve, look at the x-axis values and the area under the curve. Disregard the height (the y-axis values) of the curve. There is more on this topic in the empirical rule section. Also the normal curve is smooth. The small squiggles on the curve you see on your computer screen are from plotting in pixels. The histograms discussed in previous sections are all discrete distributions, in which the height of the bar measures frequency. Note that since the bars are all equal width, height is actually a measure of area. Thus the area concept holds for discrete distributions as well. The normal distribution is a continuous distribution because the x-axis values are not broken into specific hit or miss values.
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