Question

2. The average number of calls received by a switchboard in a 30-minute period is 5....

2. The average number of calls received by a switchboard in a 30-minute period is 5.

a. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 6 calls?

b. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 8 calls?

Please type or do not answer thank you! I have trouble reading written math.  

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The given problem is of Poisson Process.

Let the number of call received per 30 minutes be denoted by the random variable x.

It is given that = 5

The required probability is given by\

a) The probability that between 10:00 and 10:30 the switchboard will receive exactly 6 calls

We have a period (10-10:30) that is the standard 30-minute period. So,

So, the probability that between 10:00 and 10:30 the switchboard will receive exactly 6 calls is 0.14622.

b) The probability that between 10:00 and 10:30 the switchboard will receive exactly 8 calls.

So, the probability that between 10:00 and 10:30 the switchboard will receive exactly 8 calls is 0.06528.

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