The pharmacist at Arnold Palmer$$ Hospital, Wende$$ Huehn$-$Brown, receives $15$ requests for prescriptions each$$ hour, Poisson distributed. It takes her a mean time of $3$ minutes to fill$$ each, following a negative exponential distribution. The waiting line table is provided below and also we know that Wq$=$Lq$\backslash$lambda $.$

Table: Average Number of Customer in Waiting Line

Poisson$$ Arrivals, Exponential Service Times

Number of Service$$ Channels, M

$\backslash$rho

$1$

$2$

$3$

$4$

$5$

$\mathrm{.}10$

$\mathrm{.}0111$

$\mathrm{.}15$

$\mathrm{.}0264$

$\mathrm{.}0008$

$\mathrm{.}20$

$\mathrm{.}0500$

$\mathrm{.}0020$

$\mathrm{.}25$

$\mathrm{.}0833$

$\mathrm{.}0039$

$\mathrm{.}30$

$\mathrm{.}1285$

$\mathrm{.}0069$

$\mathrm{.}35$

$\mathrm{.}1884$

$\mathrm{.}0110$

$\mathrm{.}40$

$\mathrm{.}2666$

$\mathrm{.}0166$

$\mathrm{.}45$

$\mathrm{.}3681$

$\mathrm{.}0239$

$\mathrm{.}0019$

$\mathrm{.}50$

$\mathrm{.}5000$

$\mathrm{.}0333$

$\mathrm{.}0030$

$\mathrm{.}55$

$\mathrm{.}6722$

$\mathrm{.}0449$

$\mathrm{.}0043$

$\mathrm{.}60$

$\mathrm{.}9000$

$\mathrm{.}0593$

$\mathrm{.}0061$

$\mathrm{.}65$

$1\mathrm{.}2071$

$\mathrm{.}0767$

$\mathrm{.}0084$

$\mathrm{.}70$

$1\mathrm{.}6333$

$\mathrm{.}0976$

$\mathrm{.}0112$

$\mathrm{.}75$

$2\mathrm{.}2500$

$\mathrm{.}1227$

$\mathrm{.}0147$

$\mathrm{.}80$

$3\mathrm{.}2000$

$\mathrm{.}1523$

$\mathrm{.}0189$

$\mathrm{.}85$

$4\mathrm{.}8166$

$\mathrm{.}1873$

$\mathrm{.}0239$

$\mathrm{.}0031$

$\mathrm{.}90$

$8\mathrm{.}1000$

$\mathrm{.}2285$

$\mathrm{.}0300$

$\mathrm{.}0041$

$\mathrm{.}95$

$18\mathrm{.}0500$

$\mathrm{.}2767$

$\mathrm{.}0371$

$\mathrm{.}0053$

$1\mathrm{.}0$

$\mathrm{.}3333$

$\mathrm{.}0454$

$\mathrm{.}0067$

$1\mathrm{.}2$

$\mathrm{.}6748$

$\mathrm{.}0904$

$\mathrm{.}0158$

$1\mathrm{.}4$

$1\mathrm{.}3449$

$\mathrm{.}1778$

$\mathrm{.}0324$

$\mathrm{.}0059$

$1\mathrm{.}6$

$2\mathrm{.}8444$

$\mathrm{.}3128$

$\mathrm{.}0604$

$\mathrm{.}0121$

$1\mathrm{.}8$

$7\mathrm{.}6734$

$\mathrm{.}5320$

$\mathrm{.}1051$

$\mathrm{.}0227$

$2\mathrm{.}0$

$\mathrm{.}8888$

$\mathrm{.}1739$

$\mathrm{.}0398$

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

enter your response here

prescriptions $($round your response to two decimal$$ places$).$The pharmacist at Arnold Palmer$$ Hospital, Wende$$ Huehn$-$Brown, receives $15$ requests for prescriptions each$$ hour, Poisson distributed. It takes her a mean time of $3$ minutes to fill$$ each, following a negative exponential distribution. The waiting line table is provided below and also we know that Wq$=$Lq$\backslash$lambda $.$

Table: Average Number of Customer in Waiting Line

Poisson$$ Arrivals, Exponential Service Times

Number of Service$$ Channels, M

$\backslash$rho

$1$

$2$

$3$

$4$

$5$

$\mathrm{.}10$

$\mathrm{.}0111$

$\mathrm{.}15$

$\mathrm{.}0264$

$\mathrm{.}0008$

$\mathrm{.}20$

$\mathrm{.}0500$

$\mathrm{.}0020$

$\mathrm{.}25$

$\mathrm{.}0833$

$\mathrm{.}0039$

$\mathrm{.}30$

$\mathrm{.}1285$

$\mathrm{.}0069$

$\mathrm{.}35$

$\mathrm{.}1884$

$\mathrm{.}0110$

$\mathrm{.}40$

$\mathrm{.}2666$

$\mathrm{.}0166$

$\mathrm{.}45$

$\mathrm{.}3681$

$\mathrm{.}0239$

$\mathrm{.}0019$

$\mathrm{.}50$

$\mathrm{.}5000$

$\mathrm{.}0333$

$\mathrm{.}0030$

$\mathrm{.}55$

$\mathrm{.}6722$

$\mathrm{.}0449$

$\mathrm{.}0043$

$\mathrm{.}60$

$\mathrm{.}9000$

$\mathrm{.}0593$

$\mathrm{.}0061$

$\mathrm{.}65$

$1\mathrm{.}2071$

$\mathrm{.}0767$

$\mathrm{.}0084$

$\mathrm{.}70$

$1\mathrm{.}6333$

$\mathrm{.}0976$

$\mathrm{.}0112$

$\mathrm{.}75$

$2\mathrm{.}2500$

$\mathrm{.}1227$

$\mathrm{.}0147$

$\mathrm{.}80$

$3\mathrm{.}2000$

$\mathrm{.}1523$

$\mathrm{.}0189$

$\mathrm{.}85$

$4\mathrm{.}8166$

$\mathrm{.}1873$

$\mathrm{.}0239$

$\mathrm{.}0031$

$\mathrm{.}90$

$8\mathrm{.}1000$

$\mathrm{.}2285$

$\mathrm{.}0300$

$\mathrm{.}0041$

$\mathrm{.}95$

$18\mathrm{.}0500$

$\mathrm{.}2767$

$\mathrm{.}0371$

$\mathrm{.}0053$

$1\mathrm{.}0$

$\mathrm{.}3333$

$\mathrm{.}0454$

$\mathrm{.}0067$

$1\mathrm{.}2$

$\mathrm{.}6748$

$\mathrm{.}0904$

$\mathrm{.}0158$

$1\mathrm{.}4$

$1\mathrm{.}3449$

$\mathrm{.}1778$

$\mathrm{.}0324$

$\mathrm{.}0059$

$1\mathrm{.}6$

$2\mathrm{.}8444$

$\mathrm{.}3128$

$\mathrm{.}0604$

$\mathrm{.}0121$

$1\mathrm{.}8$

$7\mathrm{.}6734$

$\mathrm{.}5320$

$\mathrm{.}1051$

$\mathrm{.}0227$

$2\mathrm{.}0$

$\mathrm{.}8888$

$\mathrm{.}1739$

$\mathrm{.}0398$

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

$$

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