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eden43
01.08.2019 •
Mathematics
You are the only bank teller on duty and you want to take a break for 10 minutes but you don't want to miss any customers. suppose the arrival of customers can be models by a poisson distribution with mean of 2 customers per hour. what's the probability that 2 or more people arrive in the next 10 minutes?
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Ответ:
The probability that 2 or more people arrive in the next 10 minutes is;
P(X ≥ 2) = 0.0447
This is a poisson distribution problem with the formula;
P(X = x) = [e^(-μ) × μˣ]/x!
Where;
x is number of successes
μ is the mean in the time interval given
Since we have a mean of 2 customers per hour and want to find the probability that 2 or more people arrive in the next 10 minutes. Thus;
μ = (2 × 10)/60
μ = 0.333
Thus, probability that 2 or more people arrive in the next 10 minutes is;
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X = 0) = [e^(-0.333) × 0.333⁰]/0!
P(X = 0) = 0.7165
P(X = 2) = [e^(-0.333) × 0.333²]/2!
P(X = 2) = 0.2388
Thus;
P(X ≥ 2) = 1 - (0.7165 + 0.2388)
P(X ≥ 2) = 0.0447
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Ответ:
4.47% probability that 2 or more people arrive in the next 10 minutes
Step-by-step explanation:
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
Mean of 2 customers per hour.
What's the probability that 2 or more people arrive in the next 10 minutes?
10 minutes, so![\mu = \frac{2*10}{60} = 0.3333](/tpl/images/0158/5647/d7778.png)
Either less than two people arrive, or more than two do. The sum of the probabilities of these events is decimal 1. So
We want
. So
In which
4.47% probability that 2 or more people arrive in the next 10 minutes
Ответ:
The answer is 19342360