Question

Find the 95% confidence interval about the population mean. Enter your answer as a trilinear inequality accurate to two decimal places.

a) μ – 1.96σ ≤ x ≤ µ +1.96ơ
b) μ- 2.580 ≤ x ≤ μ +2.580
c) μ-1.650 < x < μ+1.650
d) None of the above

Answer 1

The correct answer is b) μ- 2.580 ≤ x ≤ μ +2.580.

Step-by-step explanation:

The correct answer is b) μ- 2.580 ≤ x ≤ μ +2.580.

In statistics, a confidence interval is a range of values within which we are confident the true population mean lies. The 95% confidence interval is commonly used, meaning that there is a 95% chance that the true population mean falls within this interval.

To find the 95% confidence interval about the population mean, we use the formula: μ- 2.580 ≤ x ≤ μ +2.580. The z-score for a 95% confidence level is 1.96, which is equivalent to 2.580 when multiplied by the standard deviation (σ). So, the correct answer is b) μ- 2.580 ≤ x ≤ μ +2.580.