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 μ \mu of the F-scale intensities, we use the formula:

μ=∑i=1NxiN \mu = \frac{\sum_{i=1}^N x_i}{N}

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

  • 0 0 occurs 22 22 times
  • 1 1 occurs 13 13 times
  • 2 2 occurs 2 2 times
  • 3 3 occurs 2 2 times
  • 4 4 occurs 1 1 time

The total sum of the intensities is:

∑i=1Nxi=0⋅22+1⋅13+2⋅2+3⋅2+4⋅1=0+13+4+6+4=27 \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 N = 22 + 13 + 2 + 2 + 1 = 40

Thus, the mean is calculated as:

μ=2740=0.675 \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 0 : 22 22
  • 1 1 : 13 13
  • 2 2 : 2 2
  • 3 3 : 2 2
  • 4 4 : 1 1

Observing the frequencies, we note that they start high at 22 22 for F F -scale intensity 0 0 and decrease to 1 1 for F F -scale intensity 4 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 μ=0.675 \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 B \boxed{B} .

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