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Time of the phone call is modeled with the expoential r.v with mean 12 minutes. calculate the probability that the call will last longer than half an hour.
Asked by Balaprasad Last Modified
Answer 
Mounika Kalidindi
Graduated from renowed Business school and expertise in teaching Mathematics and Physics
It is based on the concept of Exponential distribution.
Continuous random variable as it is measured- If x is the amount of time the phone call lasts which is 30 min in this scenario
As time is mean for decaying, the decaying parameter her is 1/mean = 1/12 = 0.08
So, the probability that phone call lasts for 30 minutes is = 0.08e^-0.08*30
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Score high in Math under the my guidance with 20 years teaching experience
V Sriram kumar V sriram kumar
Senior Statistics Teacher with 20 years of experience from University of Hyderabad
e^(-2.5) =0.082
read less Sanjay Tumati
IIT Grad and Chip Designer with 15 years experience
We can model the phone call with an exponential function has a Probability density Function (PDF) that can be represented as
where b>0 and the random variable 'x' represents the time taken by the phone call and f(x) represents the probability that the phone call lasts exactly 'x' hours.
Then the probability that the phone call takes less than 'y' hours is given by
If the mean call time is 12 (0.2 hours) minutes, it means that the probability that the call lasts 12 minutes (0.2 hours) or less is 0.5, Thus substituting y = 0.2, in the above equation we get
Then the probability that the call takes more than half an hour = 1-P(0.5) =
Formula for exponential distribution is : f(x) = me–mx
By replacing the variables with mean = 12 mins and by information call will last for 0.2 hours to 0.5 hours, we can get the required probability will be : 1-me–mx
So, the answer is 0.082
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