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.

the answer is d on edge

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.