Calls arrive at lynn ann fish's hotel switchboard at a rate of 2.0 per minute. the average time to handle each is 10 seconds. there is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation.1. the probability that the operator is busy = (round your response to two decimal places). 2. the average time that a caller must wait before reaching the operator = minutes (round your response to two decimal places). 3. the average number of calls waling to be answered = (round your response to two decimal places).

a)

b)

And that means 0.06 minutes for the average waiting time.

c)

And that means 0.08 minutes between each call.

Step-by-step explanation:

Previous concepts

Let X the random variable of interesr. We know that

The probability mass function for the random variable is given by:

Single Channel Queuing Model. "That division of service channels happen in regards to number of servers that are present at each of the queues that are formed. Poisson distribution determines the number of arrivals on a per unit time basis, where mean arrival rate is denoted by λ".

Data given

Arrival rate = 1.5 per minute

Service Rate = 10 seconds = 6/min

Part a

For this case we want the probability that the operator is being busy. And we can find this dividing the arrival rate by the service rate like this:

Part b

In order to find the average waiting time we can use the following formula:

Where represent the arrival rate and the service rate. If we replace we have:

And that means 0.06 minutes for the average waiting time.

Part c

In order to find the average number of call on waiting we can use the following formula:

And replacing we got:

And that means 0.08 minutes between each call.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.