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.
To sketch the normal curve, also known as the bell curve or Gaussian distribution, with the given mean and standard deviation, follow these steps:
1. Determine the values for the x-axis: The x-axis represents the variable of interest, in this case, the traffic death rates. You can choose a range that spans a few standard deviations on either side of the mean. For simplicity, let's choose a range from 2 to 8.
2. Calculate the z-scores: A z-score measures the number of standard deviations an observation is from the mean. You can calculate the z-scores using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
3. Find the corresponding probability density function (pdf) values: Using the calculated z-scores, you can find the corresponding pdf values from the standard normal distribution table or by using software like Excel, Python, or a statistical calculator.
4. Plot the normal curve: Plot the x-axis values against the corresponding pdf values to create the bell-shaped curve. The curve should be symmetric around the mean and taper off towards both tails.
5. Label the mean and standard deviation: Mark the point representing the mean on the x-axis and label it as "μ." Indicate the distance of one standard deviation on either side of the mean using vertical lines or notations such as "+σ" and "-σ" or "μ+σ" and "μ-σ".
Your completed sketch should show the normal curve, the mean (μ), and the standard deviation (σ).
Note: Without specific data points, the sketch will be a general representation of a normal curve with the given mean and standard deviation.