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## Homework Statement

Phone calls are received at Diane residence have a Poisson distribution with [tex]\lambda[/tex] =2.

a) If Diane takes a shower for 10 min, what is the probability that the phone rings Once or Twice.

b) How long can she shower if the probability of receiving no calls be at most 0.5

## Homework Equations

## The Attempt at a Solution

a) For 10 min interval [tex]\lambda[/tex] =2x(10/60)=0.33333

Probability that phone rings once-> P(X=1)= [tex] e^{-0.33333}[/tex] = 0.7166

The answer given in the book is 0.28 which it not what I am getting. Where did I go wrong?

b) P(X=0)=0.5= [tex] e^{-\Lambda}[/tex]

If I take ln of both sided I get [tex] {\Lambda}[/tex] =0.69314

The book says required time=20.79 min.

How do I get this time from the value of lambda i obtained earlier?