Probability The average time between incoming calls at a switchboard is 3 minutes. If a call has just come in, then the probability that the next call will come within the next t minutes is P ( t ) = 1 − e − t / 3 . Find the probability of each situation. (a) A call comes in within 1 2 minute. (b) A call comes in within 2 minutes. (c) A call comes in within 5 minutes.

Q: Expert Answer

(a) To determine To calculate: The probability that a call will come within 1 2 minute when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by: P ( t ) = 1 − e − t 3 Explanation Given Information: The normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by: P ( t ) = 1 − e − t 3 Calculation: Consider that the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by: P ( t ) = 1 − e − t 3 Now, the probability that a call will come within 1 2 minute. Substitute 1 2 for t in P ( t ) = 1 − e − t 3 (b) To determine To calculate: The probability that a call will come within 2 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by: P ( t ) = 1 − e − t 3 (c) To determine To calculate: The probability that a call will come within 5 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by: P ( t ) = 1 − e − t 3

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Calculus: An Applied Approach (Min...

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Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

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BuyFind

Calculus: An Applied Approach (Min...

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

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Answer 3

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Answer 4

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Answer 5

(a)

To determine

To calculate: The probability that a call will come within 12 minute when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

P(t)=1−e−t3

Explanation of Solution

Given Information:

The normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

P(t)=1−e−t3

Calculation:

Consider that the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

P(t)=1−e−t3

Now, the probability that a call will come within 12 minute.

Substitute 12 for t in P(t)=1−e−t3

Answer 6

(b)

To determine

To calculate: The probability that a call will come within 2 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

P(t)=1−e−t3

Answer 7

(c)

To determine

To calculate: The probability that a call will come within 5 minutes when the normal time between the inbound calls at a switchboard is 3 minutes and the probability that the next call would come within the next t minutes if a call has recently come is given by:

P(t)=1−e−t3

Calculus: An Applied Approach (Min...

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Calculus: An Applied Approach (Min...

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