Answer
n= 10, $\bar{x}$ = 48.6 years, σ = 4.1, $z_α/_2$ = 1.96
When Confidence interval = 95%
α= 1-0.95 = 0.05.
α/2 = 0.025
1-0.025 = 0.975
From the table,
$z_α/_2$ = 1.96
The 95% confidence interval of the mean for all students:
$\bar{x}$ - $z_α/_2$($\frac{σ}{\sqrt n}$ )< μ < $\bar{x}$ - $z_α/_2$( $\frac{σ}{\sqrt n}$ )
= 48.6 - 1.96( $\frac {4.1}{\sqrt 10}$ < μ < 48.6 + 1.96( $\frac {4.1}{\sqrt 10}$
= 46.06 years < μ < 51.14 years