Answer
The probability that the mean score of your sample is between 20 and 30 is 0.9996.
Work Step by Step
Here we have n = 25, μ = 25, x̅ = 20 & 30, σ = 6.5
$σ_{x̅} = \frac{σ}{\sqrt n} = \frac{25 }{\sqrt 6.5} = 1.3$
Using the z-value approach, we have:
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{20-25}{1.3} = -3.486$
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{30-25}{1.3} = 3.486$
Using Table A of the book, we have:
P(-3.486 < z < 3.486) = 0.9996
