(a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (Round your answers to four decimal places.) at least 2 hours x at most 3 hours 0.7113 0.1481 between 2 and 3 hours (b) What is the probability that rainfall duration exceeds the mean value by more than 3 standard deviations? (Round your answer to four decimal places.) x

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Q16

**Understanding Rainfall Duration Using Exponential Distribution**

Data collected at an airport suggests that an exponential distribution with a mean value of 2.415 hours is a good model for rainfall duration.

### (a) Probability Calculations for Specific Rainfall Durations:

1. **What is the probability that the duration of a particular rainfall event at this location is:**
   - **At least 2 hours?**
     - Probability: 0.7113
  
   - **At most 3 hours?**
     - Probability: 0.7212
  
   - **Between 2 and 3 hours?**
     - Probability: 0.1481

*Note: Probabilities are rounded to four decimal places.*

### (b) Probability for Rainfall Duration Exceeding the Mean Value by More Than 3 Standard Deviations:

**Question: What is the probability that rainfall duration exceeds the mean value by more than 3 standard deviations?**
- **Answer:** (answer is not provided in the image-blank field)

*In the context of this calculation, you'll need to input this information correctly rounded to four decimal places.*

This page provides an educational overview of applying exponential distributions to real-world scenarios, specifically focusing on pattern analysis of rainfall duration at an airport.
Transcribed Image Text:**Understanding Rainfall Duration Using Exponential Distribution** Data collected at an airport suggests that an exponential distribution with a mean value of 2.415 hours is a good model for rainfall duration. ### (a) Probability Calculations for Specific Rainfall Durations: 1. **What is the probability that the duration of a particular rainfall event at this location is:** - **At least 2 hours?** - Probability: 0.7113 - **At most 3 hours?** - Probability: 0.7212 - **Between 2 and 3 hours?** - Probability: 0.1481 *Note: Probabilities are rounded to four decimal places.* ### (b) Probability for Rainfall Duration Exceeding the Mean Value by More Than 3 Standard Deviations: **Question: What is the probability that rainfall duration exceeds the mean value by more than 3 standard deviations?** - **Answer:** (answer is not provided in the image-blank field) *In the context of this calculation, you'll need to input this information correctly rounded to four decimal places.* This page provides an educational overview of applying exponential distributions to real-world scenarios, specifically focusing on pattern analysis of rainfall duration at an airport.
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