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

Step-by-step 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 :-

$z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}$

For p= 0.60

$z=\dfrac{0.60-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{447}}}\approx1.70$

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

$P(x$

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