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Chapter 5: Q. 53 (page 351)

A customer service representative must spend different

amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be

modelled by the following distribution:X~Exp(0.2)

Find P(2<x<10).

Short Answer

Expert verified

The answer ofP(2<x<10)=0.5350

Step by step solution

01

Function of exponential distribution

As per the Function, P(x<x)=1-e-mx

Wherex~Exp(0.2)

Therefore,m=0.2

02

Step 2. Formula of exponential  

P(2 < x < 10)= P(x < 10) - P(x<2)

Applying all data

P(2 < x < 10 =(1-e0.2脳10)-(1-e0.2脳2)

=0.6703-0.1353=0.5350

The answer of role="math" localid="1648208427638" P(2<x<10)=0.5350

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98. During the years 1998-2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.

a. What is the probability that the next earthquake occurs within the next three months?

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d. What is the probability that at least two earthquakes will occur in 2014 ?

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