Answer
$P(X\gt100)=0.0764$
Work Step by Step
For a random sample of 25 we have:
$μ_{X ̅}=μ=90$
$σ_{X ̅}=\frac{σ}{\sqrt n}=\frac{35}{\sqrt {25}}=7$
Let's find the z-score for 100:
$z=\frac{X-μ_{X ̅}}{σ_{X ̅}}=\frac{100-90}{7}=1.43$
According to Table V, the area of the standard normal curve to the left of z-score equal to 1.43 is 0.9236.
But, we want the area of the standard normal curve to the right of z-score equal to 1.43:
$1-0.9236=0.0764$
