(a) 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

Bundle: Calculus: An Applied Approach, Brief, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

10th Edition

ISBN: 9781337604826

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 4.2, Problem 43E

(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

(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

(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

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Chapter 4.2, Problem 42E

Chapter 4.2, Problem 44E

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Chapter 4 Solutions

Bundle: Calculus: An Applied Approach, Brief, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the properties of exponents to simplify each...Ch. 4.1 - Use the formula for the ratio of carbon isotopes...Ch. 4.1 - Prob. 4CP Ch. 4.1 - Prob. 5CP Ch. 4.1 - Prob. 1SWU Ch. 4.1 - Prob. 2SWU Ch. 4.1 - Prob. 3SWU Ch. 4.1 - Prob. 4SWU Ch. 4.1 - Prob. 5SWU

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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

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

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

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

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Chapter 4 Solutions

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

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

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