A political pollster is conducting an analysis of sample results in order to mak

Question

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least

53% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 400 voters

What is is the probability that a canidate will be forecast as the winner when the population percentage of her vote is 50.1%

What is is the probability that a canidate will be forecast as the winner when the population percentage of her vote is 57%

What is is the probability that a canidate will be forecast as the winner when the population percentage of her vote is 49%

Explanation / Answer

a.
Proportion ( P ) =0.501
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.501*0.499/400)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X >= 0.53) = (0.53-0.501)/0.025
= 0.029/0.025 = 1.16
= P ( Z >1.16) From Standard Normal Table
= 0.123                  
b.
Proportion ( P ) =0.57
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.57*0.43/400)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 0.53) = (0.53-0.57)/0.0248
= -0.04/0.0248 = -1.6129
= P ( Z >-1.613) From Standard Normal Table
= 0.9466                  
c.
Proportion ( P ) =0.49
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.49*0.51/400)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 0.53) = (0.53-0.49)/0.025
= 0.04/0.025 = 1.6
= P ( Z >1.6) From Standard Normal Table
= 0.0548                  

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