Now, let's suppose the National Disaster Management Authority (NDMA) wants to start evacuating people from low-lying regions if the rainfall in August exceeds 2,000 mm. What is the probability that the NDMA would undertake evacuation activities? (µ = 1,600 mm and σ = 400 mm)
Question
Now, let's suppose the National Disaster Management Authority (NDMA) wants to start evacuating people from low-lying regions if the rainfall in August exceeds 2,000 mm. What is the probability that the NDMA would undertake evacuation activities? (µ = 1,600 mm and σ = 400 mm)
Solution
To find the probability that the NDMA would undertake evacuation activities, we can use the concept of standard deviation and the normal distribution.
Step 1: Calculate the z-score The z-score is a measure of how many standard deviations an observation or value is from the mean. In this case, we want to find the z-score for a rainfall of 2,000 mm.
The formula to calculate the z-score is: z = (x - µ) / σ
Where: x = rainfall value (2,000 mm) µ = mean rainfall (1,600 mm) σ = standard deviation (400 mm)
Plugging in the values, we get: z = (2,000 - 1,600) / 400 z = 400 / 400 z = 1
Step 2: Find the probability Once we have the z-score, we can use a standard normal distribution table or a calculator to find the corresponding probability.
Looking up the z-score of 1 in the standard normal distribution table, we find that the probability is approximately 0.8413.
Therefore, the probability that the NDMA would undertake evacuation activities if the rainfall in August exceeds 2,000 mm is approximately 0.8413 or 84.13%.
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