Question

A population proportion is 0.40. A random sample of size 100 will be taken and the sample proportion p will be used to estimate the population proportion. Use the z-table. Round your answers to four decimal places. a. What is the probability that the sample proportion will be within ±0.04 of the population proportion? b. What is the probability that the sample proportion will be within ±0.05 of the population proportion?

Answer 1

To find the probability that the sample proportion will be within ±0.04 of the population proportion, calculate the z-score using the formula (p - p') / sqrt((p * q) / n) and use the z-table to find the corresponding cumulative probability.

Step-by-step explanation:

To find the probability that the sample proportion will be within ±0.04 of the population proportion, we need to calculate the z-score for ±0.04 using the z-table. The z-score is calculated as (p - p') / sqrt((p * q) / n), where p is the population proportion, p' is the sample proportion, q is 1 - p, and n is the sample size.

Once we have the z-score, we can look it up in the z-table to find the corresponding cumulative probability. Since we want the probability for both the upper and lower bounds, we need to find the area under the curve for both z-scores.