City and State
The city and state that I chose for this week’s discussion post is Cleveland, Ohio. Cleveland is located on the southern shore of Lake Erie. The lake moderates the city’s climate. More specifically, Lake Erie keeps the temperatures in Cleveland generally cooler in summer and warmer in winter. In addition, the lake occasionally causes heavy “lake” effect winter snows. The average number of days of precipitation in Cleveland was 14 (“Average Precipitation in US Cities During April,” n.d). Using the average number of days of precipitation in Cleveland during April, the probability of having exactly ten days, less than three days, and more than 15 days of precipitation in Cleveland in April will be calculated.
Calculations
Let,
i.e.,
Based on Poisson distribution, the probability of having precipitation on “x” number of days is given by the following formula:
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(
Özel & Inal, C. (2010)
In our case,
Therefore,
What is the probability of having exactly 10 days of precipitation in the month of April?
What is the probability of having less than three days of precipitation in the month of April?
What is the probability of having more than 15 days of precipitation in the month of April?
Analysis
The probability of having exactly 10 days of precipitation in April in Cleveland is 0.0663. This means that Cleveland is 6.63 percent likely to have exactly ten days of precipitation in April. The probability that Cleveland will have less than three days of precipitation in April was also calculated and found to be 0.00009396. This means that it is 0.009396 percent likely that Cleveland will experience less than three days of precipitation in April. The probability that Cleveland will have more than 15 days of precipitation during the month of April was also calculated and found to be 0.3306. This means that it is 33.06 percent likely that Cleveland will have more than 15 days of precipitation in April.
To determine if an event is usual or unusual, one has to check if the probability is less or greater than 5 percent first. If the probability if greater than 5 percent, then the event is usual and vice versa. The event that Cleveland will experience less than three days of precipitation is unusual. This is because the probability, which is 0.009396 percent, is less than 5 percent. However, the events that Cleveland will have exactly ten days of precipitation, and more than 15 days of precipitation is usual. This is because of their probabilities, which are 6.63 and 33.06 percent, respectively, are higher than 5 percent.
References
Average Precipitation in US Cities During April. (n.d.). https://www.currentresults.com/Weather/US/average-precipitation-by-city-in-april.php
Özel, G., & Inal, C. (2010). The probability function of a geometric Poisson distribution. Journal of Statistical Computation and Simulation , 80 (5), 479-487.
