Answer:
(a)
(b)
(c) P(X ≤ 1) = 0.6321
(d) P(2 ≤ X ≤ 5) = 0.1286
Step-by-step explanation:
From the given information; Let consider X to be the time between two successive arrivals at the drive-up window of a local bank.
However; If X is regarded as the exponential distribution with λ = 1 which is identical to a standard gamma distribution with ∝ = 1
The objective is to compute the following :
(a) The expected time between two successive arrivals is;
(b) The standard deviation of the time between successive arrivals is;
(c) P(X ≤ 1)
P(X ≤ 1) = 1 - e⁻¹
P(X ≤ 1) = 0.6321
(d) P(2 ≤ X ≤ 5)
P(2 ≤ X ≤ 5) = [1 - e⁻⁵] - [1 - e⁻²]
P(2 ≤ X ≤ 5) = 0.9933 - 0.8647
P(2 ≤ X ≤ 5) = 0.1286
