Solution Found!
The time to failure (in hours) for a laser in a cytometry
Chapter 4, Problem 198SE(choose chapter or problem)
The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with \(\lambda=0.00004\). What is the probability that the time until failure is
(a) At least 20,000 hours? (b) At most 30,000 hours?
(c) Between 20,000 and 30,000 hours?
Equation transcription:
Text transcription:
\lambda=0.00004
Questions & Answers
QUESTION:
The time to failure (in hours) for a laser in a cytometry machine is modeled by an exponential distribution with \(\lambda=0.00004\). What is the probability that the time until failure is
(a) At least 20,000 hours? (b) At most 30,000 hours?
(c) Between 20,000 and 30,000 hours?
Equation transcription:
Text transcription:
\lambda=0.00004
ANSWER:Solution :
Step 1 of 3:
Let X denotes the failure time for laser in cytometry machine following exponential distribution with .
The exponential density function is
f(x) = , x
0
Our goal is:
a). We need to find the probability that at least 20,000 hours.
b). We need to find the probability that at most 30,000 hours.
c). We need to find the probability that between 20,000 and 30,000 hours.
a). The probability of at least 20,000 hours is
P(X>20000) =
P(X>20000) =
P(X>20000) =
P(X>20000) =
P(X>20000) =
P(X>20000) =
P(X>20000) = 0.4493
Therefore, the probability of at least 20,000 hours is 0.4493.