SOLUTION: Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of getting 251 heads or less.

Question 165388: Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of getting 251 heads or less.
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
using normal curve approximation:
n = 500
p = .5
x = 251
s (standard deviation) = sqrt(500*.5*.5) = sqrt(125) = 11.18033989
z = (x-n*p)/s
n*p = 500 * .5 = 250
x = 251
x-n*p = 251-250 = 1
(x-n*p)/s = 1/11.18033989 = .089442719
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using the online z table evaluator, probability of getting 251 heads or less is
.535635
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that would be the area under the curve for values less than .089442719 with the mean = 0 and the standard deviation = 1
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since n*p = mean of normal distribution, you will get the same answer if you plug in a mean of 250 and an s (standard deviation) of 11.18033989 and you ask for the area under the curve for all values of x less than 251.
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z table evaluator can be found at:
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http://davidmlane.com/hyperstat/z_table.html
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