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SVEN [57.7K]
2 years ago
14

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. th

ere is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation. what is the probability, as a percent, that the operator is busy
Mathematics
1 answer:
BartSMP [9]2 years ago
4 0

The probability that the operator is busy is 33.33% if the call rate is 2 per minute and average time to handle is 10 seconds.

Given rate of calls 2 per minute and average time to handle a call is 10 seconds.

We have to find the probability that the operator is busy.

Probability is the chance of happening an event among all the events possible. The value of probability lies between 0 and 1.

Probability= number of items/ total items

If rate is 2 per minute then the customers handled in 1 hour=2*60=120

The average time to handle a call=10 seconds.

Therefore customers to be handled in 1 hour=360 (10*6*60)

Probability that the operator is busy is as under:

Probability=λ/μ

=120/360

=1/3

=1/3*100

=33.33%

Hence the probability that the operator is busy is 33.33%.

Learn more about probability at brainly.com/question/24756209

#SPJ4

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Justin gave the clerk $20 to pay a bill of $6.57. How much change will Justin get
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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (
True [87]
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16 

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two. 

If you wanted to, you could check your answer by finding g(x).  Since you know g'(x), take the antiderivative and we will get 
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer.  Not a bad method if you ever need to use it. 
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