Asked by Leo Elvis
The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes. what is the probability that a). it will take a technician less than 10 minutes to fix a computer problem? b) it will take a technician between 10 to 15 minutes to fix a computer problem?
Answers
Answered by
MathMate
Exponential distribution has mean = λ
where λ is the number of occurrences in a unit time, say one hour.
So λ=60/15=4
The exponential probability distribution function is given by:
P(T=t)=λe<sup>-λt</sup>
and the cumulative distribution function:
P(T<t)=1-e<sup>-λt</sup>
(a) repairing in less than 10 minutes (i.e. 1/6 hour),
P(T<1/6)
=1-e<sup>-4/6</sup>
=1-.5134
=0.4866
(b) repairing between 10 to 15 minutes:
15 minutes = 1/4 hour
10 minutes = 1/6 hour
P(X<1/4)-P(X<1/6) = ?
where λ is the number of occurrences in a unit time, say one hour.
So λ=60/15=4
The exponential probability distribution function is given by:
P(T=t)=λe<sup>-λt</sup>
and the cumulative distribution function:
P(T<t)=1-e<sup>-λt</sup>
(a) repairing in less than 10 minutes (i.e. 1/6 hour),
P(T<1/6)
=1-e<sup>-4/6</sup>
=1-.5134
=0.4866
(b) repairing between 10 to 15 minutes:
15 minutes = 1/4 hour
10 minutes = 1/6 hour
P(X<1/4)-P(X<1/6) = ?
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.