Subjects statistics

Rainfall Probability D582F2

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1. **Problem statement:** We are given that the average rainfall per season is 35 inches with a standard deviation of 4 inches. We want to find the probability that next year the rainfall will be at most 40 inches. 2. **Formula and concept:** This is a problem involving the normal distribution. The rainfall amount $X$ is normally distributed with mean $\mu = 35$ and standard deviation $\sigma = 4$. 3. We want to find $P(X \leq 40)$. 4. **Step 1: Standardize the variable** using the z-score formula: $$z = \frac{X - \mu}{\sigma}$$ 5. Calculate the z-score for $X=40$: $$z = \frac{40 - 35}{4} = \frac{5}{4} = 1.25$$ 6. **Step 2: Use the standard normal distribution table** or a calculator to find $P(Z \leq 1.25)$. 7. From the standard normal table, $P(Z \leq 1.25) \approx 0.8944$. 8. **Interpretation:** There is approximately an 89.44% chance that the rainfall will be at most 40 inches next year. **Final answer:** 0.8944 (option b)