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

Click here to see ALL problems on Probability-and-statistics

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
-----
using the online z table evaluator, probability of getting 251 heads or less is
.535635
-----
that would be the area under the curve for values less than .089442719 with the mean = 0 and the standard deviation = 1
----
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.
-----
z table evaluator can be found at:
-----
http://davidmlane.com/hyperstat/z_table.html
-----