The different probabilities and number of callers expected to be waiting are;
A) P(x = 3) = 0.0286
B) P(x = 13) = 0.1056
C) 8 will be waiting
D) P(x = 0) = 0.0003
E) P(x = 0) = 0.0067
<h3>How to find probability using Poisson distribution?</h3>
We are given the rate of 48 phone calls per hour.
Thus, we will use poisson's distribution formula;
P(x) = (λˣ × e^(-λ))/x!
A) Probability of receiving three calls in a 10-minute interval of time which is P(x = 3). Thus;
λ = 48 * (10/60)
λ = 8
P(x = 3) = (8³ × e⁻⁸)/3!
P(x = 3) = 0.0286
B) Probability of receiving exactly 13 calls in 15 minutes is P(x = 13). Thus;
λ = 48 * (15/60)
λ = 12
P(x = 13) = (12¹³ × e⁻¹²)/13!
P(x = 13) = 0.1056
C) No calls are currently on hold and it takes 10 minutes to complete one call. Thus;
λ = 48 * (10/60)
λ = 8
Thus, 8 will be waiting after 10 minutes.
D) Probability that no one will be waiting is;
P(x = 0) = (8⁰ × e⁻⁸)/0!
P(x = 0) = 0.0003
E) No calls being processed and it takes 5 minutes for a personal time without being interrupted by a call. Thus;
λ = 48 * (5/60)
λ = 4
P(x = 0) = (4⁰ × e⁻⁵)/0!
P(x = 0) = 0.0067
Read more about probability with poisson's distribution at; brainly.com/question/7879375
