The normal curve is a graphical representation of the distribution of data. The curve is symmetrical and has a peak at the mean value. As the mean increases, the curve approaches the normal distribution, but it never quite reaches it. This phenomenon is known as the asymptote.
As the mean of a normal distribution increases, the graph of the distribution becomes more bell-shaped. This is because as the mean gets larger, more and more data points are pulled towards the center of the curve. The graph becomes flatter as the mean increases because there are fewer extreme data points at either end of the curve.
If you want to understand how the normal curve shifts as mean increases, first let me tell you what a normal curve looks like.
A normal curve is a probability distribution where the area under the curve (or integral of the density function) is always 1. This can be seen by drawing the area under the curve.
When you add up all the areas under the curve, the sum must be 1. This means that the area under the curve must always be greater than or equal to zero. Therefore, when the mean is negative, the area under the curve is positive. When the mean is zero, the area under the curve is zero. When the mean is positive, the area under the curve is negative.
As the mean gets more positive, the curve gets steeper. This can be seen by graphing the mean as the y-axis and the area under the curve as the x-axis. The slope of the line connecting the two points is the ratio of the y-intercept to the slope. The slope of the line is the rate of change of the area under the curve with respect to the mean. As the mean gets more positive, the slope gets steeper.
For example, if you have a sample of 20 people with the following data, the mean is the average height in inches.
The slope of the line connecting the two points is the ratio of the y-intercept to the slope. The slope of the line is the rate of change of the area under the curve with respect to the mean.
Since the mean of the sample is 4.7, the slope of the line is 1/3.
Thus, the area under the curve is 3.6.
Now look at the graph of the normal curve.
The mean of the normal curve is 4.7. Notice that the area under the curve is 3.6.
So the area under the curve is less than the area under the normal curve as the mean gets more positive.
The difference between the areas can be calculated by subtracting the area under the normal curve from the area under the curve.
So the difference between the two areas is 0.6.
Thus, if the mean gets more positive, the area under the curve gets less than the area under the normal curve.
This means that the normal curve shifts to the left as the mean becomes more positive.
This is how a normal curve shifts when the mean becomes more positive.
The graph of the normal curve shifts to the right as the mean increases. This means that the curve becomes taller and more narrow, with a greater number of scores bunched together at the top. As a result, the probability of obtaining scores above or below a certain point decreases.
