Suppose $\mu$ = 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

Given the population mean (μ) = 50 and the population standard deviation (σ) = 10, for a sample size (n) = 100, the standard error of the mean (σ_x̄) = σ / √n = 10 / √100 = 1. The 95% confidence interval for the sample mean is calculated using the formula μ ± 1.96*σ_x̄, which equals 50 ± 1.96*1 = 50 ± 1.96 = 48.04 to 51.96. This means 95% of all possible sample means will indeed fall between 48.04 and 51.96.

Suppose μ\muμ = 50 And σ\sigmaσ = 10 for a Population

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