On average, 40 customers are visiting a store in an hour. Find the probability of more than 40 customers visiting that store in an hour. (15 p)
I am not going to just do these for you. I already took the subject (in 1958). What are your answers?
To find the probability of more than 40 customers visiting the store in an hour, we need to use the concept of the Poisson distribution. The Poisson distribution is often used to model the number of events that occur in a fixed interval of time or space, given the average rate of occurrence.
In this case, the average rate of occurrence is 40 customers per hour. Let's denote this average rate by λ (lambda).
The formula to calculate the probability of k events occurring in a Poisson distribution is:
P(X = k) = (e^(-λ) * λ^k) / k!
where e is the mathematical constant approximately equal to 2.71828.
Since we want to find the probability of more than 40 customers visiting the store, we need to calculate the sum of probabilities for k values greater than 40.
P(X > 40) = 1 - P(X <= 40)
To be efficient, we can utilize the cumulative distribution function (CDF) of the Poisson distribution to avoid summing probabilities individually.
Using a calculator or a statistical software, you can compute the probability directly by plugging in the values into the formula.
Alternatively, if you prefer manual calculations, you can find the probability by calculating the CDF for values less than or equal to 40 and subtracting it from 1.
I hope this explanation helps you understand the process of calculating the probability of more than 40 customers visiting the store in an hour using the Poisson distribution.