Answer
$p = 0.9998 \approx 1$
Work Step by Step
Here, we have n = 1000, $μ = μ_{x̅} = 115$, σ = 25
$σ_{x̅} = \frac{σ}{\sqrt n} = \frac{25 }{\sqrt 1000} = 0.79$
We need to calculate the z score for the probability that x̅ takes a value between 112 and 118 mg/dL.
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{112-115}{0.79} = -3.8$
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{118-115}{0.79} = 3.8$
Using Table A of the book, we have:
P(-3.8 < z < 3.8) = P(z < 3.8) - P(z > 3.82) = 0.9999 - 0.0001 = 0.9998
