Final answer:
The question asks for the probability of having no customers awaiting service when service times follow an exponential distribution and arrivals are Poisson distributed. However, none of the provided answer choices match the calculated probability of 0.1111, suggesting an error in the question or that additional information is required to determine the exact answer.
Step-by-step explanation:
The student's question involves finding the probability that there are no customers waiting when service times are exponentially distributed and arrivals follow a Poisson distribution. Given that customers arrive at a rate of 200 per hour and it takes 4 minutes to serve a customer, we can calculate this probability using the formulas for these distributions.
To solve, first we need to know the service rate (μ) which is the number of customers that can be served per hour. Since there are 15 service providers (Tatiana plus her 14 assistants), and each can serve a customer in 4 minutes, the service rate is 15 providers multiplied by the number of customers one provider can serve in an hour (60/4 = 15 customers per hour per provider).
Thus, μ = 15 providers x 15 customers/provider/hour = 225 customers/hour.
The arrival rate (λ) given is 200 customers per hour.
Using a queueing theory formula for the probability of having no customers in the system P(0) = 1 - (λ/μ), we calculate P(0) = 1 - (200/225), which equals 0.1111. This probability does not match any of the answer choices (A, B, C, D), indicating a possible error in the question or that further context is required for a precise answer.