Suppose X has an exponential distribution with mean equal to 13. Determine the following: (a) P(X > 10) (Round your answer to 3 decimal places.) (b) P(X> 20) (Round your answer to 3 decimal places.) (c) P(X < 30) (Round your answer to 3 decimal places.)
Suppose X has an exponential distribution with mean equal to 13. Determine the following: (a) P(X > 10) (Round your answer to 3 decimal places.) (b) P(X> 20) (Round your answer to 3 decimal places.) (c) P(X < 30) (Round your answer to 3 decimal places.)
A First Course in Probability (10th Edition)
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![### Exponential Distribution Problem
**Problem Statement:**
Suppose \( X \) has an exponential distribution with mean equal to 13. Determine the following:
**Questions:**
(a) \( P(X > 10) \)
- (Round your answer to 3 decimal places.)
(b) \( P(X > 20) \)
- (Round your answer to 3 decimal places.)
(c) \( P(X < 30) \)
- (Round your answer to 3 decimal places.)
(d) Find the value of \( x \) such that \( P(X < x) = 0.95 \).
- (Round your answer to 2 decimal places.)
**Answer Inputs:**
(a) \[ \quad \]
(b) \[ \quad \]
(c) \[ \quad \]
(d) \[ \quad \]
**Explanation:**
In problems (a) through (c), you are required to calculate probabilities for events related to the exponential distribution. In problem (d), you need to determine the value of \( x \) that corresponds to a cumulative probability of 0.95.
Please take care to round your final answers to the specified number of decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F028d8221-c1da-48bc-9506-b7b935324171%2F94162310-06ca-4aa3-8ee1-b2a9d6dfea1b%2Fpym2mi_processed.png&w=3840&q=75)
Transcribed Image Text:### Exponential Distribution Problem
**Problem Statement:**
Suppose \( X \) has an exponential distribution with mean equal to 13. Determine the following:
**Questions:**
(a) \( P(X > 10) \)
- (Round your answer to 3 decimal places.)
(b) \( P(X > 20) \)
- (Round your answer to 3 decimal places.)
(c) \( P(X < 30) \)
- (Round your answer to 3 decimal places.)
(d) Find the value of \( x \) such that \( P(X < x) = 0.95 \).
- (Round your answer to 2 decimal places.)
**Answer Inputs:**
(a) \[ \quad \]
(b) \[ \quad \]
(c) \[ \quad \]
(d) \[ \quad \]
**Explanation:**
In problems (a) through (c), you are required to calculate probabilities for events related to the exponential distribution. In problem (d), you need to determine the value of \( x \) that corresponds to a cumulative probability of 0.95.
Please take care to round your final answers to the specified number of decimal places.
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