Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials"+ proposes a Poisson distribution for X. Suppose that μ = 4. (Round your answers to three decimal places.) (a) Compute both P(X ≤ 4) and P(X < 4). P(X ≤ 4) = P(X < 4) = (b) Compute P(4 ≤ x ≤ 6). (c) Compute P(6 ≤ X).
Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials"+ proposes a Poisson distribution for X. Suppose that μ = 4. (Round your answers to three decimal places.) (a) Compute both P(X ≤ 4) and P(X < 4). P(X ≤ 4) = P(X < 4) = (b) Compute P(4 ≤ x ≤ 6). (c) Compute P(6 ≤ X).
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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![Let \( X \) be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials" proposes a Poisson distribution for \( X \). Suppose that \( \mu = 4 \). (Round your answers to three decimal places.)
(a) Compute both \( P(X \leq 4) \) and \( P(X < 4) \).
\[
P(X \leq 4) = \text{ }
\]
\[
P(X < 4) = \text{ }
\]
(b) Compute \( P(4 \leq X \leq 6) \).
\[
\text{ }
\]
(c) Compute \( P(6 \leq X) \).
\[
\text{ }
\]
(d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation?
\[
\text{ }
\]
You may need to use the appropriate table in the Appendix of Tables to answer this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F324f16c4-c4e5-4b06-b074-f261b39e021a%2Faa0c4816-53d6-428a-9b74-72eafad8be52%2Fq6kzqsx_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( X \) be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodology for Probabilistic Life Prediction of Multiple-Anomaly Materials" proposes a Poisson distribution for \( X \). Suppose that \( \mu = 4 \). (Round your answers to three decimal places.)
(a) Compute both \( P(X \leq 4) \) and \( P(X < 4) \).
\[
P(X \leq 4) = \text{ }
\]
\[
P(X < 4) = \text{ }
\]
(b) Compute \( P(4 \leq X \leq 6) \).
\[
\text{ }
\]
(c) Compute \( P(6 \leq X) \).
\[
\text{ }
\]
(d) What is the probability that the number of anomalies does not exceed the mean value by more than one standard deviation?
\[
\text{ }
\]
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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