# Thread: Find Xₒ where P(X ≥Xₒ) = 0.65 and X ~ N(200,15)

1. ## Find Xₒ where P(X ≥Xₒ) = 0.65 and X ~ N(200,15)

I'm currently taking Statistics 1 and I'm stuck on a problem that I've been trying to solve out for a while...hopefully one of you guys can help me out...heres the question:
Find Xwhere P(X ≥X) = 0.65 and X ~ N(200,15)

-From population draw a sample of 36 units. Find P(x-bar ≥ 225)
-Construct a confidence interval at 95% confidence
-Interpret the interval ask that on the physics forum

2. First of all, is 15 the variance or st deviation? I guess its the st deviation since it's not a perfect square.

$.65=P( X>x_0 )=P\left(Z>{x_0-200\over 15}\right)$

Next look up the 65 LOWER percentile, z0 of a st normal and solve for x0 ...

$z_0={x_0-200\over 15}$

3. Originally Posted by matheagle
First of all, is 15 the variance or st deviation? I guess its the st deviation since it's not a perfect square.

$.65=P( X>x_0 )=P\left(Z>{x_0-200\over 15}\right)$

Next look up the 65 LOWER percentile, z0 of a st normal and solve for x0 ...

$z_0={x_0-200\over 15}$

sorry i still don't understand, could u plz explain.
thankx

4. Originally Posted by desiclub07
I'm currently taking Statistics 1 and I'm stuck on a problem that I've been trying to solve out for a while...hopefully one of you guys can help me out...heres the question:
Find Xwhere P(X ≥X) = 0.65 and X ~ N(200,15)

[snip]
Use tables or whatever way you've been taught to get the number $z_0$ such that $\Pr(Z \geq z_0) = 0.65$ where Z is the standard normal random variable.

Substitute into $z_0 = \frac{x_0 - 200}{15}$ and solve for $x_0$.

Note: $\Pr(Z \geq z_0) = 0.65 \Rightarrow \Pr(Z < z_0) = 0.35 \Rightarrow \Pr(Z > -z_0) = 0.35 \Rightarrow \Pr(Z \leq -z_0) = 0.65$. Therefore $-z_0 = ..... \Rightarrow z_0 = .....$