We require a sample size of no less than 75. Step-by-step explanation: Given that the population variance is 484, we are tasked with determining the needed sample size for maintaining a margin of error of 5 or less. The formula for margin of error is as follows: Margin of error = [calculation]. Here, the significance level equals 1 - 0.95, which is 0.05, making [corresponding value] = 0.025. Additionally, the standard deviation, calculated using [variance], equals 22. At the 0.025 significance level, the critical value from the z table is 1.96. Therefore, the margin of error equals [calculations]. By squaring both sides, we derive: n = [calculation]. Hence, a sample size of at least 75 is required.
A minimum sample size of 75 is necessary. Step-by-step explanation: We need to determine our level, which is calculated by subtracting 1 from the confidence interval divided by 2. Now, we need to find the z value in the Z table that corresponds to a p-value of [Z value]. Therefore, it is the z value with a p-value of [specific value]. Next, we calculate the margin of error M, where [insert equation], with [standard deviation] representing the population standard deviation and n as the sample size. The standard deviation equals the square root of the variance. With a 0.95 probability level, if the margin of error desired is 5 or below, a sample size of at least 75 is required.
