Questions: The accompanying data set lists the F-scale intensities of recent tornadoes in the United States. Construct a frequency distribution. Do the intensities appear to have a normal distribution? Assume that the intensities are quantitative. Click the icon to view the F-scale intensities. Complete the frequency distribution. F-Scale Intensity Frequency 0 22 1 13 2 2 3 2 4 1 (Type whole numbers.) Do the intensities appear to have a normal distribution? A. No, because while the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, the distribution is not symmetric. B. No, because the frequencies start at a maximum and become low, and because the distribution is not symmetric. C. No, because while the distribution is approximately symmetric, the frequencies start at a maximum and become low. D. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.

The accompanying data set lists the F-scale intensities of recent tornadoes in the United States. Construct a frequency distribution. Do the intensities appear to have a normal distribution? Assume that the intensities are quantitative.

Click the icon to view the F-scale intensities.

Complete the frequency distribution.

F-Scale Intensity  Frequency 
0  22 
1  13 
2  2 
3  2 
4  1 

(Type whole numbers.)
Do the intensities appear to have a normal distribution?
A. No, because while the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, the distribution is not symmetric.
B. No, because the frequencies start at a maximum and become low, and because the distribution is not symmetric.
C. No, because while the distribution is approximately symmetric, the frequencies start at a maximum and become low.
D. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.
Transcript text: The accompanying data set lists the F-scale intensities of recent tornadoes in the United States. Construct a frequency distribution. Do the intensities appear to have a normal distribution? Assume that the intensities are quantitative. Click the icon to view the F-scale intensities. Complete the frequency distribution. \begin{tabular}{c|c} \hline F-Scale Intensity & Frequency \\ \hline 0 & 22 \\ \hline 1 & 13 \\ \hline 2 & 2 \\ \hline 3 & 2 \\ \hline 4 & 1 \\ \hline \end{tabular} (Type whole numbers.) Do the intensities appear to have a normal distribution? A. No, because while the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, the distribution is not symmetric. B. No, because the frequencies start at a maximum and become low, and because the distribution is not symmetric. C. No, because while the distribution is approximately symmetric, the frequencies start at a maximum and become low. D. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.
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Solution

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Solution Steps

Step 1: Calculate the Mean

To find the mean \( \mu \) of the F-scale intensities, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the total number of observations and \( x_i \) are the individual values. Given the frequency distribution:

  • \( 0 \) occurs \( 22 \) times
  • \( 1 \) occurs \( 13 \) times
  • \( 2 \) occurs \( 2 \) times
  • \( 3 \) occurs \( 2 \) times
  • \( 4 \) occurs \( 1 \) time

The total sum of the intensities is:

\[ \sum_{i=1}^N x_i = 0 \cdot 22 + 1 \cdot 13 + 2 \cdot 2 + 3 \cdot 2 + 4 \cdot 1 = 0 + 13 + 4 + 6 + 4 = 27 \]

The total number of observations is:

\[ N = 22 + 13 + 2 + 2 + 1 = 40 \]

Thus, the mean is calculated as:

\[ \mu = \frac{27}{40} = 0.675 \]

Step 2: Analyze the Distribution

Next, we analyze the frequency distribution to determine if it appears to follow a normal distribution. The frequencies are as follows:

  • \( 0 \): \( 22 \)
  • \( 1 \): \( 13 \)
  • \( 2 \): \( 2 \)
  • \( 3 \): \( 2 \)
  • \( 4 \): \( 1 \)

Observing the frequencies, we note that they start high at \( 22 \) for \( F \)-scale intensity \( 0 \) and decrease to \( 1 \) for \( F \)-scale intensity \( 4 \). This pattern indicates that the distribution is not symmetric and does not resemble the bell curve characteristic of a normal distribution.

Final Answer

The mean of the F-scale intensities is \( \mu = 0.675 \). The intensities do not appear to have a normal distribution because the frequencies start at a maximum and decrease, indicating a lack of symmetry.

The answer is \( \boxed{B} \).

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