Answer
0.7698
Work Step by Step
Here, we have n = 100, $μ = μ_{x̅} = 115$, σ = 25
$σ_{x̅} = \frac{σ}{\sqrt n} = \frac{25 }{\sqrt 100} = 2.5$
We need to calculate the z score for the probability that x̅ takes a value between 112 and 118 mg/dL.
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{112-115}{2.5} = -1.2$
$z = \frac{x̅ - μ_{x̅}}{σ_{x̅}} = \frac{118-115}{2.5} = 1.2$
Using Table A of the book, we have:
P(-1.2 < z < 1.2) = P(z < 1.2) - P(z > -1.2) = 0.8849 - 0.1151 = 0.7698
