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Answer: 8.96%
## Explanation To find the probability that X lies outside the range between 12 and 61, we need to calculate the probability that X < 12 or X > 61. ### Step 1: Calculate z-scores For X = 12: $$z_1 = \frac{12 - 40}{14} = \frac{-28}{14} = -2$$ For X = 61: $$z_2 = \frac{61 - 40}{14} = \frac{21}{14} = 1.5$$ ### Step 2: Find probabilities using standard normal distribution - P(z < -2) = 0.0228 - P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668 ### Step 3: Calculate total probability Total probability = P(z < -2) + P(z > 1.5) = 0.0228 + 0.0668 = 0.0896 Converting to percentage: 0.0896 × 100% = 8.96% Therefore, the probability that X lies outside the range between 12 and 61 is 8.96%.
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A quantitative analyst is building a model whose output depends on the value of a financial variable, X. The analyst assumes X is a random variable that follows a normal distribution with a mean of 40 and a standard deviation of 14. What is the probability that X lies outside the range between 12 and 61?
A
4.56%
B
6.18%
C
8.96%
D
18.15%
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