# Thread: normal distribution with a mean and standard deviation...I am lost

1. ## normal distribution with a mean and standard deviation...I am lost

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)

2. 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!

3. Originally Posted by caligirl350
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)
Sorry, but these are very routine questions - I suggest you go to your class notes or textbook and review the examples that are certain to be there.