Question

Suppose 60% of the registered voters in a country are Democrats. If a sample of 793 voters is selected, what is the probability that the sample proportion of Democrats will be greater than 64%? Round your answer to four decimal places.

Answer 1

To calculate the probability that the sample proportion of Democrats will be greater than 64%, we can use the normal distribution approximation. The probability is approximately 0.0458 or 4.58%.

Step-by-step explanation:

To calculate the probability that the sample proportion of Democrats will be greater than 64%, we can use the normal distribution approximation. The mean of the sample proportion is equal to the population proportion, which is 60%, and the standard deviation of the sample proportion is given by:

sqrt((p*(1-p))/n)

where p is the population proportion and n is the sample size. Plugging in the values, we have:

sqrt((0.6*(1-0.6))/793) = 0.01427

We can then use the z-score formula to find the probability:

P(Z > (0.64 - 0.6)/0.01427)

Calculating this probability using a standard normal distribution table or calculator, we find that the probability is approximately 0.0458 or 4.58%.