Question

Suppose 56% of the registered voters in a country are Republican. If a sample of 447 voters is selected, what is the probability that the sample proportion of Republicans will be less than 60%? Round your answer to four decimal places.

Answer 1

Answer: 0.9554

Explanation:

Given : The proportion of the registered voters in a country are Republican = P=0.56

The number of voters = 447

The test statistic for proportion :-

`z=\frac{p-P}{\sqrt{(P(1-P))/(n)}}`

For p= 0.60

`z=\frac{0.60-0.56}{\sqrt{(0.56(1-0.56))/(447)}}\approx1.70`

Now, the probability that the sample proportion of Republicans will be less than 60% (by using the standard normal distribution table):-

`P(x<0.60)=P(z<1.70)=0.9554345\approx0.9554`

Hence, the probability that the sample proportion of Republicans will be less than 60% = 0.9554