The pharmacist at Arnold Palmer$$ Hospital, Wende$$ Huehn$-$Brown, receives requests for prescriptions each$$ hour, Poisson distributed. It takes her a mean time of minutes to fill$$ each, following a negative exponential distribution. The waiting line table is provided below and also we know that

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Part $2$

$$a$)$ Using the$$ table, the average number of prescriptions in the queue$=$

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enter your response here prescriptions $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ Using the given$$ relationship, the average time a prescription spends in the queue$=$

$$

enter your response here minutes $($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ Wende decides to hire a second$$ pharmacist, Ajay$$ Aggerwal, whom she went to school with and who operates at the same speed in filling prescriptions. Using the$$ table, the average number of prescriptions in the queue$=$

$$

enter your response here prescriptions $($round your response to two decimal$$ places$).$

Part $5$

Using the given$$ relationship, the average time a prescription spends in the queue after Wende has hired Ajay Agarwal$=$

$$

enter your response here minutes $($round your response to two decimal$$ places$).$