Suppose ? = 50 and $\sigma$ = 10 for a population.In a sample where n = 100 is randomly taken,95% of all possible sample means will fall between 48.04 and 51.96.

Question

Quizplus · Accepted Answer

This statement is true based on the given information and the properties of the normal distribution. The sample mean will have a normal distribution with mean μ and standard deviation σ/√n. Using the given values, we can find that this standard deviation is 10/√100 = 1. Therefore, the interval from 48.04 to 51.96 is a 95% confidence interval for the true population mean, meaning that we can be 95% confident that the true population mean falls in this range.

Suppose ? = 50 And σ\sigmaσ = 10 for a Population

Suppose ? = 50 And $\sigma$ = 10 for a Population