Answer:
58,21 ≤ μ ≤ 61,79
Step-by-step explanation:
Normal Distribution
Poputation size n = 41
Population mean X = 60
Population standard deviation σ = 7
Question is: Confidence Interval 90 % ??
As Confidence Interval is 90 % then α = 10 %
And as we are dealing with a two tail test
α/2 = 0,05
We look in Z table for values for α/2 = 0,05 and find
z(α/2) = - 1,64 and z(α/2) = 1,64
Then
Confidence Interval is
X - Zα/2 * σ/√n ≤ μ ≤ X + Zα/2 * σ/√n
60 - ( 1,64 ) * 7/√41 ≤ μ ≤ 60 + ( 1,64 ) * 7/√41
60 - 1,64 * 1,09375 ≤ μ ≤ 60 + 1,64 * 1,09375
60 - 1,79375 ≤ μ ≤ 60 + 1,79375
58,21 ≤ μ ≤ 61,79
