From historical data, it was found that the rainfall received by Kerala in the month of August was normally distributed with a mean of 1,600 mm and a standard deviation of 400 mm. Let’s suppose that floods are caused when the rainfall in August exceeds 2,400 mm. What is the probability that the state would experience a flood?
Question
From historical data, it was found that the rainfall received by Kerala in the month of August was normally distributed with a mean of 1,600 mm and a standard deviation of 400 mm. Let’s suppose that floods are caused when the rainfall in August exceeds 2,400 mm. What is the probability that the state would experience a flood?
Solution
To find the probability of the state experiencing a flood, we need to calculate the area under the normal distribution curve that represents rainfall exceeding 2,400 mm.
Step 1: Standardize the value of 2,400 mm using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. z = (2,400 - 1,600) / 400 z = 800 / 400 z = 2
Step 2: Look up the z-score in the standard normal distribution table or use a calculator to find the corresponding probability. The probability associated with a z-score of 2 is approximately 0.9772.
Step 3: Subtract the probability from 1 to find the probability of rainfall exceeding 2,400 mm. P(rainfall > 2,400 mm) = 1 - 0.9772 P(rainfall > 2,400 mm) ≈ 0.0228
Therefore, the probability that the state of Kerala would experience a flood in August is approximately 0.0228 or 2.28%.
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