Answer questions $1-6$ based on the following data.

For an M$/$G$/1$ system with $\backslash$lambda $=20,\backslash$mu $=35,$ and $\backslash$sigma $=0\mathrm{.}005.$

Find the probability the system is idle.

Group of answer choices

P$0=0\mathrm{.}4286$

P$0=0\mathrm{.}3926$

P$0=0\mathrm{.}964$

P$0=0\mathrm{.}6095$

Question $2$

Find the average length of the queue.

Group of answer choices

Lq $=0\mathrm{.}4286$

Lq $=0\mathrm{.}3926$

Lq $=0\mathrm{.}964$

Lq $=0\mathrm{.}6095$

Question $3$

Find the average number in the system.

Group of answer choices

L $=0\mathrm{.}4286$

L $=0\mathrm{.}3926$

L $=0\mathrm{.}964$

L $=0\mathrm{.}6095$

Question $4$

Find the average time a unit spends in the waiting line.

Group of answer choices

Wq $=0\mathrm{.}0214$

Wq $=0\mathrm{.}0196$

Wq $=0\mathrm{.}0482$

Wq $=0\mathrm{.}0305$

Question $5$

Find the average time a unit spends in the system.

Group of answer choices

W $=0\mathrm{.}0500$

W $=0\mathrm{.}0482$

W $=0\mathrm{.}0768$

W $=0\mathrm{.}0590$

Question $6$

Find the probability that an arriving unit has to wait for service.

Group of answer choices

Pw $=0\mathrm{.}5714$

Pw $=0\mathrm{.}4286$

Pw $=0\mathrm{.}6095$

Pw $=0\mathrm{.}3905$

Question $7$

Arrivals at a box office in the hour before the show follow the Poisson distribution with $\backslash$lambda $=7$ per minute. Service times are constant at $7\mathrm{.}5$ seconds. Find the average length of the waiting line.

Group of answer choices

Lq $=3\mathrm{.}0625$

Lq $=4\mathrm{.}845$

Lq $=1\mathrm{.}056$

Lq $=2\mathrm{.}5258$