Question

the sample population is normally distributed, ¯x=42.5, σ = 3, and n = 30. What is the 90% confidence interval for µ?

Answer 1

$90\%CI=(\bar x-z_{0.05}\frac{\sigma}{\sqrt{n}},\bar x+z_{0.05}\frac{\sigma}{\sqrt{n}})=$

$=(42.5-1.645\frac{3}{\sqrt{30}},42.5+1.645\frac{3}{\sqrt{30}})=(41.60,43.40).$