SOLUTION: I need to solve this problem using De Moivre - Laplace theorem and I am stuck with it. When throwing a coin the chance of it being heads is 0.52. If a person gets heads - they s

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Question 1192606: I need to solve this problem using De Moivre - Laplace theorem and I am stuck with it.
When throwing a coin the chance of it being heads is 0.52. If a person gets heads - they step to the right, if tails - steps to the left. What is the probability that after 1015 steps person will be no more than 58 steps away from the starting point? More than 58 steps to the right?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
what is 57 steps to either side? The midpoint is 507.5, so one wants 565/450 OR 450/565. This means that we want the number of steps to the right between 450 and 565.
can do a normal approximation
np=mean=1015*0.52=527.8. The mean number of steps to the right is 20.3
variance is np(1-p)=253.34
sd=sqrt (V)=15.92
z=(x-mean)/sd so z>(-57.5-20.3)/15.92 and z<(57.5-20.3)/15.92. The .5 on each is for the continuity correction factor used when approximating a mass function with a continuous one.
z is between -4.89 and 2.34
This has probability of 0.9904 (last digit might change depending upon where you round z.)
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for more than 58 steps to the right, the probability is 0.0096.