Just before a referendum on a school budget a local newspape

Just before a referendum on a school budget, a local newspaper polls 444 voters to predict whether the budget will pass. Suppose the budget has the support of 53% of the voters. What is the probability that the newspaper\'s sample will lead it to predict defeat? The probability is

Solution

Normal Distribution
Proportion ( P ) =0.53
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.53*0.47/444)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.5) = (0.5-0.53)/0.0237
= -0.03/0.0237= -1.2658
= P ( Z <-1.2658) From Standard Normal Table
= 0.103