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February 22nd, 2011, 09:45 PM  #1 
Member Joined: Dec 2010 From: Drachten, the Netherlands Posts: 49 Thanks: 0  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= (0.57.5)/squareroot(7.125) = 2.622, corresponding probability: 0.004371 and z= (1.57.5)/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 0.0122940.004371= 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= (6.57)/squareroot(3.5) = 0.26726, corresponding probability: 0.394634 and z= (7.57)/squareroot(3.5) = 0.26726 corresponding probability; 0.394634 So the answer is 2*0.50.394634=.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 
February 22nd, 2011, 11:40 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: two easy to solve approximation problems
I agree with your answers...


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