X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
(A) P(x < 77.0)
(B) P(75.0 < x < 85.0)
(C) P(x > 85.0)
A)
Find the z value fot x = 77.
$\displaystyle z = \dfrac{x - \mu}{\sigma} = \dfrac{77 - 80}{3.5} = -0.857$
So, you have
$\displaystyle P(X < 77) = P(z < -0.857)$
Look up your z table for the corresponding probability.
Do the same for the others.
B) $\displaystyle P(75.0 <X< 85.0) = P(\dfrac{75 - 80}{3.5} < z < \dfrac{85 - 80}{3.5}) = P( -1.429 < z < 1.429)$
C) $\displaystyle P(X > 85.0) = P(z > 1.429)$
Post what you get!