Final answer:
To find the probability that a sample proportion will be within 0.05 of the population proportion, use the standard deviation formula for sample proportions.
Step-by-step explanation:
To find the probability that a sample proportion will be within 0.05 of the population proportion, we can use the standard deviation formula for sample proportions. The standard deviation formula for sample proportions is:
Standard Deviation (σ) = √[p * (1-p) ÷ n]
where:
- p is the population proportion
- n is the sample size
Using this formula, we can calculate the standard deviation for each sample size and then find the probability using the z-score formula.