Can someone please help me with this problem also?
A study of motor vehicle rates in the 50 states reveals that traffic death rates (deaths per 100 million motor vehicle miles driven) can be modeled by the normal curve. The data suggest that the distribution has a mean of 5.3 and a standard deviation of 1.3. Sketch the normal curve, showing the mean and standard deviation.
It cant be much different that this:
http://davidmlane.com/hyperstat/z_table.html
To sketch the normal curve representing the traffic death rates, you can follow these steps:
Step 1: Understand the parameters
The parameters provided are the mean (μ) and standard deviation (σ) of the distribution. In this case, the mean is 5.3 and the standard deviation is 1.3.
Step 2: Determine the range
Since the problem does not specify the range of the distribution, you will need to decide on an appropriate range based on the context or the given data. Let's assume a range of 0 to 10 for simplicity.
Step 3: Plot the axes
Draw a horizontal axis (X-axis) representing the range of the distribution (0 to 10) and a vertical axis (Y-axis) representing the frequency or probability density.
Step 4: Find the mean
Locate the mean (μ = 5.3) on the X-axis and mark it with a vertical line. This represents the center point of the distribution.
Step 5: Find the standard deviation
To find the standard deviation, you can use the empirical rule or the z-scores. Since the empirical rule applies to normal distributions, it will help you estimate the spread of the data.
According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
To determine the spread, draw two vertical lines above and below the mean at one standard deviation (1.3) intervals. In this case, draw two lines above the mean at 6.6 and 7.9, and two lines below the mean at 3.4 and 2.1. These represent the boundaries of one standard deviation.
Step 6: Sketch the curve
To sketch the curve, connect the points marked at the boundaries of one standard deviation using a smooth, symmetrical curve. Make sure the curve is centered on the mean.
The resulting sketch should show a bell-shaped curve centered at 5.3, with the curve tapering off towards both ends.
Remember, this is a rough sketch to visualize the distribution based on the given parameters. For a more accurate representation, you may need more precise data or a broader range of values.