28 The number of customers arriving per
commercial bank for service facility is
i= 17.
hour at Arba Minch town main branch off Ethiopian
assumed to follow a Poisson distribution with mean
Compute the probability that exactly
20 customers will arrive in a given hour period.
(b) Compute the probability that more than 10 customers will arrive in a 2-hour period.
To compute the probability that exactly 20 customers will arrive in a given hour period, we can use the formula for the probability mass function (PMF) of a Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!
Where X is the random variable representing the number of customers arriving, λ is the mean number of customers per hour (17 in this case), and k is the desired number of customers (20 in this case).
So, plugging in the values:
P(X = 20) = (e^(-17) * 17^20) / 20!
Calculating this expression will give us the probability.
To compute the probability that more than 10 customers will arrive in a 2-hour period, we can use the cumulative distribution function (CDF) of the Poisson distribution:
P(X > k) = 1 - P(X <= k)
So, in this case, we want to find P(X > 10) for a 2-hour period. We can use the fact that the sum of independent Poisson random variables with the same mean follows a Poisson distribution with a mean equal to the sum of the individual means. In this case, the mean for a 2-hour period would be 2 * λ = 34.
P(X > 10) = 1 - P(X <= 10)
P(X <= 10) can be calculated using the PMF of the Poisson distribution with a mean of 34, and then subtracting it from 1 will give us the desired probability.