One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average rate of 2.4 calls per minute.a. If an operator wants to take a one-minute break, what is the probability that there will be no calls during a one-minute interval?b. If an operator can handle at most five calls per minute, what is the probability that the operator will be unable to handle the calls in any one-minute period?c. What is the probability that exactly three calls will arrive in a two-minute interval?d. What is the probability that one or fewer calls will arrive in a 15-second interval? a. P(x = 0 | λ = 2.4) = b. P(x > 5 | λ = 2.4) = c. P(x = 3 | λ = 4.8) = d. P(x ≤ 1 | λ = 0.6) =
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average rate of 2.4 calls per minute.
a. If an operator wants to take a one-minute break, what is the
b. If an operator can handle at most five calls per minute, what is the probability that the operator will be unable to handle the calls in any one-minute period?
c. What is the probability that exactly three calls will arrive in a two-minute interval?
d. What is the probability that one or fewer calls will arrive in a 15-second interval?
a. P(x = 0 | λ = 2.4) =
b. P(x > 5 | λ = 2.4) =
c. P(x = 3 | λ = 4.8) =
d. P(x ≤ 1 | λ = 0.6) =
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