Answer :
The likelihood of getting more than three messages in a 2-minute period is 0.051.
Define binomial counting.
A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.
Given,
Understanding the answer to the presented problem requires knowledge of the binomial counting process, the usage of frames and the arrival rate of events to calculate matching probability values.
An interactive message center's electronic message volume is modelled using a binomial counting procedure with 15-second frames. One message arrives on average per minute.
Let's use to denote the average arrival rate.
1 minute is equal to (1)
There are four 15-second frames in a minute because the unit is minutes.
When, Δ= 14 and Δ = Frame length
The probability of a message within an interval of two minutes is then determined by
p = λ∆ = 1 x ¼
p = ¼ → (2)
Let X(n) be the total number of successfully delivered messages at the end of the nth frame.
n = 1,2,3… and X(0)= 0.
In other words,
p(x(n) = x) = u px (1-p)n-x
We already know the answers to this problem:
p = 1/4,
x = 3,
and n = 4.
There are four 15-second frames total.
p(x (4) > 3) = 1-p [x(4) < 3]
px4=0+px4=1+p(x4=2) = 1-
1-(0.3164 + 0.422 + 0.211)
1-0.9491
p(x (4) > 3) = 0.051 → (3)
The likelihood of getting more than three messages in a 2-minute period is 0.051.
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