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$$ Question $2$ of $10$

Question $2$

$1$ points

At a police station, citizens are arriving at a pace of four per hour. Currently, just one officer is available to help these individuals, and it takes this officer twelve minutes to assist each one. The officer overseeing the station is contemplating the addition of another officer to aid the incoming citizens. As stipulated by the supervising officer, the key condition for this change is that adding another officer must reduce the total time taken to assist each citizen by five minutes. Only the second officer will be assigned this duty if this criterion is met. Given this situation, assuming that arrivals are Poisson distributed and service times are exponentially distributed, which of the following answers is correct? $($Note: Assume that the second officer will have the same 'service time rate' as the first officer.$)$

The second officer should be reassigned to this duty because it will reduce the total time by $45$ minutes.

The second officer should be reassigned to this duty because it will reduce the total time by $15$ minutes

Only one officer should stay on to this duty because it is already less than five minutes.

Only one officer should stay on to this duty because it is already five minutes.