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Answer:
a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.
b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the binomial distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Poisson process with rate 2 per minute
This means that
a. What is the probability that during a given 1 min period, the first operator receives no requests?
Single operator, so we use the Poisson distribution.
This is P(X = 0).
0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.
b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?
6 operators, so we use the binomial distribution with
Each operator has a 13.5% probability of receiving no requests during a minute, so
This is P(X = 3).
0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests