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February 22nd, 2011, 09:45 PM   #1
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two easy to solve approximation problems

I really hope that someone can help me by looking very critical at my answers.
I am getting really frustated. I have no idea what I do wrong but my answers are different from the answers from the book.
Some are almost the same, but not totally. So maybe I make a little mistake. Please tell me what I do wrong

Use the normal approximation to the binomial distributoin to determine b(1,150,0.05)
This is my answer:
mean = 150*0.05=7.5
sigma = squareroot(150*0.05* 0.95) =squareroot (7.125)
Since I have to find P(X=1), I used the continuity correction
z= (0.5-7.5)/squareroot(7.125) = -2.622, corresponding probability: 0.004371
and z= (1.5-7.5)/squareroot(7.125) = -2.2478 corresponding probability; 0.012294
I used a z calculator in order to be very precise about the probabilities.

So the answer is 0.012294-0.004371= 7.923 X 10^-3
However according to the book the answer is 8.7 X 10^-3

the following frustiating problem is:
Use the normal approximation to the binomial distributoin to determine the probability of getting 7 heads and 7 tail in 14 flips of a balanced coin.
This is my answer:
mean = 14*0.5=7
sigma = squareroot(14*0.5* 0.5) =squareroot (3.5)
Since I have to find P(X=7), I used the continuity correction
z= (6.5-7)/squareroot(3.5) = -0.26726, corresponding probability: 0.394634
and z= (7.5-7)/squareroot(3.5) = 0.26726 corresponding probability; 0.394634

So the answer is 2*0.5-0.394634=.210732
However according to the book the answer is 0.2128


I my perception there are both the same kind of problem. Since in both cases my answer is not equal to the one of the bank I am afraid that I make a fundamental mistake. So i hope that someone can look critical at it in order to help me.

Thanks in advance
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February 22nd, 2011, 11:40 PM   #2
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Re: two easy to solve approximation problems

I agree with your answers...
aswoods is offline  
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