Let us say that,
X = the number of residents in the sample who favor
annexation.
X has a distribution which follows a binomial curve with parameters:
n=50 and p=0.29
Calculating for mean:
Mean of X = n * p = 50 * 0.29
Mean of X = 14.5
Calculating for standard deviation:
Standard deviation of X = sqrt(n * p * (1 - p))
Standard deviation of X = 3.2086
Now we are to find the probability that at least 35% favour
annexation:
35% * 50 = 17.5 residents
Normal approximation can be applied in this case since sample size is greater
than 31. Therefore,
Required Probability:
P(X>=17.5) = 1 - P(X<17.5)
1 - P(z<(17.5-14.5)/3.2086) = 1 - P(z<0.9350) = 1- 0.825106 = 0.174894
Answer:
0.175 or 17.5%
