Question

Suppose 50% of the registered voters in a country are Republican.

If a sample of 629 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by less than 4%? Round your answer to four decimal places.

Answer 1

Solution:-

The probability that the sample proportion of Republicans will differ from the population proportion by less than 4% is 0.9556

p₁ = 0.50 - 0.04 = 0.46

p₂ = 0.50 + 0.04 = 0.54

By applying normal distribution:-

z₁ = - 2.01

z₂ = 2.01

P( -2.01 < z < 2.01) = P(z > -2.01) - P(z > 2.01)

P( -2.01 < z < 2.01) = 0.9778 - 0.0222

P( -2.01 < z < 2.01) = 0.9556