Final answer:
To find the required probability using the sampling distribution of the proportion, calculate the z-score using the formula and use it to find the probability.
Step-by-step explanation:
To find the required probability using the sampling distribution of the proportion, we need to calculate the z-score and then use it to find the corresponding probability. The formula for calculating the z-score is:
z = (p - P') / sqrt((P' * (1 - P')) / n)
Where p is the proportion of interest, P' is the estimated proportion, and n is the sample size. Once we have the z-score, we can use a standard normal distribution table, calculator, or statistical software to find the probability.
For example, if we want to find the probability that the proportion is less than a certain value, we can use the formula:
Probability = z-score
By rounding the answer to four decimal places, we can obtain the required probability.