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February 4th, 2011, 07:54 AM   #1
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From: Drachten, the Netherlands

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the amount of money it takes the be served

The amount of time it takes a person to be served at a given restaurant is a random variable with the probability density

f(x)=1/4e^(-x/4) for x>0

What can we assert about the amount of time it takes a person to be served at the given restuarand if we use chebyshev's theorem with k=1.5. What is the corresponding probability rounded to four decimals?

I found E(X) = 4 and the standard deviation is also 4.

according to chebyshec's theorem the change is at least 1-1/1.5^2= 5/9 that the time it takes is between 0 and 10 minutes ( 4-1.5*4 (however have to be >0)<X<4+1.5k).

The exact probability is I think -e^(-10/4) --e^(0) = 0.9279

I this both correct?
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