1. ## normal distribution

Q) Y~N(50,sigma^2), P(Y>40)=0.6554, find sigma.

I have a rough idea of how to do it and i know the answer is sigma=25 but i cannot get to this answer just wondering if someone could please break it down for me so i can see where i am going wrong.

thanks

2. Originally Posted by wahhdoe

Q) Y~N(50,sigma^2), P(Y>40)=0.6554, find sigma.

I have a rough idea of how to do it and i know the answer is sigma=25 but i cannot get to this answer just wondering if someone could please break it down for me so i can see where i am going wrong.

thanks
Get the z-value z* such that $\displaystyle \Pr(Z > z*) = 0.6554$ (you should have been taught how to do this). Note that z* < 0 (why is this obvious?).

Then $\displaystyle \displaystyle z* = \frac{40 - 50}{\sigma}$. Solve for $\displaystyle \sigma$.

3. thats what ive tried but this gives me z*=0.4 is there something i have done wrong there because then i would solve sigma=-25 when the answer is +25??

4. Originally Posted by wahhdoe
thats what ive tried but this gives me z*=0.4 is there something i have done wrong there because then i would solve sigma=-25 when the answer is +25??
If you read my first reply, you will see that I even went to the trouble of warning you that z* < 0. Is your value of z* less than zero?

5. no my value of z*=0.4

6. Originally Posted by wahhdoe
no my value of z*=0.4
I can see that. But what I'm telling you is that your value is wrong. How can z* possibly be greater than zero when the value for Y is less than the mean?!

You have made a mistake. Unless you accept this fact and then show your working on how you got this incorrect value, I have nothing more to say.