Question
In: Statistics and Probability
The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate...
The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate at which calls were coming through was 1.5 per minute.
a. What is the probability that no call came through in a one-minute period?
b. What is the probability that less than 180 calls came through in a two-hour period?
Solutions
Expert Solution
The poisson distribution have probability as 
, where the mean is lambda. The mean rate of calls is 1.5/min, and
hence, the probability would be 
, for probability of x calls coming in a minute.
(a) The probability that zero calls came
through in a minute will be 
or 
. Hence, there is a 22.313% chance that no call came in a
minute.
(b) The average rate of calls is 1.5 per
minute, and hence in two hours or 120 mins, the mean rate would be
1.5*120=180 calls per 2 hour. Probability of x calls coming in 2
hours is 
.
The probability that less than 180 calls came in those 2 hours
is 
or 
. It can be calculated only by the help of any online calculator or
via r, excel. I have used an online calculator, with the parameters
x=180 and lambda=180, and we have 
. Hence, there are 49.01% chances of occuring that.
orchestra answered 2 years agoRelated Solutions
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