If the mean rate of arrival in a restaurant is 10 customers per hour, what is the probability of having 4 customers arriving in any hour?
What is your measure of variability?
I have answer this question as follow:
P(C)=(ac*e-a)/c!=(104*e-10)/4!=
(10000*e-10)/24=(10000*2.71828-10)/24= (10000*4.5406)/24=0.45406/24=0.0185
Is it correct?
To determine the probability of having a certain number of customers arriving in an hour, we can use the Poisson distribution. The Poisson distribution is usually used to model the number of events occurring in a fixed interval of time or space, given the average rate at which they occur.
In this case, the mean rate of arrival is given as 10 customers per hour. Let's denote this as λ (lambda) = 10.
The formula for the probability of having exactly k events occur in a time interval, given the average rate λ, is:
P(k) = (e^-λ * λ^k) / k!
Where e is a mathematical constant approximately equal to 2.71828.
So, to find the probability of having exactly 4 customers arriving in any hour in this restaurant, we substitute k = 4 and λ = 10 into the formula:
P(4) = (e^-10 * 10^4) / 4!
Calculating this probability requires evaluating the exponential function and performing factorial calculations, which can be complex. However, you can use a scientific calculator, statistical software, or programming language to simplify the calculations for you.
Alternatively, you can use online Poisson probability calculators, which allow you to input the lambda value and the number of events you're interested in, and they will give you the corresponding probability.