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?

Answer 1

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^-λt
and the cumulative distribution function:
P(T<t)=1-e^-λt

(a) repairing in less than 10 minutes (i.e. 1/6 hour),

P(T<1/6)
=1-e^-4/6
=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) = ?