SOLUTION: A coin is loaded so that the chance of getting heads in a single toss is 0.6. If the coin is tossed four hundred times, estimate the probability of getting exactly two hundred and

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Question 924165: A coin is loaded so that the chance of getting heads in a single toss is 0.6. If the coin is tossed four hundred times, estimate the probability of getting exactly two hundred and ninety heads.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
It is obviously so unlikely that it would be exactly 290 times out of 400
that the probability would be so close to 0 that it would be negligible.

mu=mean+=+np+=+400%280.6%29+=+240

sigma=standard_deviation+=+sqrt%28np%281-p%29%29=sqrt%28400%2A0.6%2A%281-0.6%29%29+=+0.798

So we want P(289.5 < x < 290.5)

You can get that with z-scores and a normal table by finding

P(x < 289.5) - P(x < 290.5)

which is

P(z < 5.052) - P(z < 5.154)

Too small to find on any table.  So it has no significance.
It is very nearly impossible, though not quite impossible.

Maybe once in 100 years!

Edwin