A certain standardized test has math Scores that are normally distributed with a mean score of 20 and a standard deviation of 3. A random sample of 9 math scores are collected. Find μ_x ̅ .

Answer 1

Let μ = 20, σ = 3, and n = 9 math scores. We don't know X as an actual math score and z-score. We can assume we are 95% confident that the math score is between the lower value and the upper value.

z = (X - 20)/(3/√9) = (X - 20)/1 = X - 20

Based on the assumption, the z-critical value will be 1.96. Therefore, we have ±1.96 = X - 20.

X = [20 - 1.96, 20 + 1.96] = [18.04, 21.96]

The math score will be more than 18 and less than 22.