To construct a probability model for the month in which tornadoes occurred in 2017, follow these steps:
Step 1: Sum the total number of tornadoes recorded over all months.
Step 2: Calculate the probability for each month by dividing the number of tornadoes in that month by the total number of tornadoes.
Step 3: Round this result to three decimal places.
Referring to the tornado data for each month, let's fill in the probabilities:
1. January: Tornadoes = 40
2. February: Tornadoes = 24
3. March: Tornadoes = 53
4. April: Tornadoes = 211
5. May: Tornadoes = 237
6. June: Tornadoes = 243
7. July: Tornadoes = 124
8. August: Tornadoes = 90
9. September: Tornadoes = 63
10. October: Tornadoes = 99
11. November: Tornadoes = 64
12. December: Tornadoes = 224
The total number of tornadoes is:
[tex]\[40 + 24 + 53 + 211 + 237 + 243 + 124 + 90 + 63 + 99 + 64 + 224\][/tex]
Next, calculate the probability for each month by dividing the number of tornadoes in that month by the total number of tornadoes (sum of all tornadoes), and then round to three decimal places.
- January:
[tex]\[
P(\text{January}) = \frac{40}{total \, tornadoes} \approx 0.027
\][/tex]
- February:
[tex]\[
P(\text{February}) = \frac{24}{total \, tornadoes} \approx 0.016
\][/tex]
- March:
[tex]\[
P(\text{March}) = \frac{53}{total \, tornadoes} \approx 0.036
\][/tex]
- April:
[tex]\[
P(\text{April}) = \frac{211}{total \, tornadoes} \approx 0.143
\][/tex]
- May:
[tex]\[
P(\text{May}) = \frac{237}{total \, tornadoes} \approx 0.161
\][/tex]
- June:
[tex]\[
P(\text{June}) = \frac{243}{total \, tornadoes} \approx 0.165
\][/tex]
- July:
[tex]\[
P(\text{July}) = \frac{124}{total \, tornadoes} \approx 0.084
\][/tex]
- August:
[tex]\[
P(\text{August}) = \frac{90}{total \, tornadoes} \approx 0.061
\][/tex]
- September:
[tex]\[
P(\text{September}) = \frac{63}{total \, tornadoes} \approx 0.043
\][/tex]
- October:
[tex]\[
P(\text{October}) = \frac{99}{total \, tornadoes} \approx 0.067
\][/tex]
- November:
[tex]\[
P(\text{November}) = \frac{64}{total \, tornadoes} \approx 0.043
\][/tex]
- December:
[tex]\[
P(\text{December}) = \frac{224}{total \, tornadoes} \approx 0.152
\][/tex]
So, your completed probability model is:
\begin{tabular}{|l|c|}
\hline Month & Probability \\
\hline 1 (January) & 0.027 \\
\hline 2 (February) & 0.016 \\
\hline 3 (March) & 0.036 \\
\hline 4 (April) & 0.143 \\
\hline 5 (May) & 0.161 \\
\hline 6 (June) & 0.165 \\
\hline 7 (July) & 0.084 \\
\hline 8 (August) & 0.061 \\
\hline 9 (September) & 0.043 \\
\hline 10 (October) & 0.067 \\
\hline 11 (November) & 0.043 \\
\hline 12 (December) & 0.152 \\
\hline
\end{tabular}
