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 3 years ago
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