a. What is the probability that a service time is less than or equal to one minute (to 4 decimals)?"
The exponential distribution probability is given by the formula:
[tex]P(T \leq t) = 1 - e^{-\lambda t} [/tex]
where:
λ = average in unit time = 1/2.2 = 0.45 services per minute
t = time requested = 1 minute
[tex]P(T \leq 1) = 1 - e^{-0.45} [/tex]
p(T ≤ 1) = 0.3624
Hence, the probability that a service time is less than or equal to one minute is p = 0.3624, which means 36.24%.
