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.
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.
Solution
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:
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.