A passenger metal detector at Chicagos Midway Airport gives

A passenger metal detector at Chicago\'s Midway Airport gives an alarm 0.40 times a minute.

a.) Find the median waiting time until the next alarm (in minutes)

b.) Find the first quartile of waiting time before the next alarm

c.) Find the 75th percentile waiting time until the next alarm

Solution

Given X~Exponential distribution with mean=0.4

F(x)=1-exp(-0.4x) for x>0

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a.) Find the median waiting time until the next alarm (in minutes)

F(x)=1-exp(-0.4x)=0.5

--> exp(-0.4x)=1-0.5=0.5

--> -0.4x=log(0.5)

So x= log(0.5)/-0.4 =1.732868

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b.) Find the first quartile of waiting time before the next alarm

F(x)=1-exp(-0.4x)=0.25

--> exp(-0.4x)=1-0.25=0.75

--> -0.4x=log(0.75)

So x= log(0.75)/-0.4 =0.7192052

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c.) Find the 75th percentile waiting time until the next alarm

F(x)=1-exp(-0.4x)=0.75

--> exp(-0.4x)=1-0.75=0.25

--> -0.4x=log(0.25)

So x= log(0.25)/-0.4 =3.465736