Hey there, I have two fairly simple questions for you, one I have an answer that id like checked, the other I need more help with

Women's Weight are normally distributed with a mean of 143 & a standard deviation of 29lb.

a)If one woman is randomly Selected, find the probability that her weight will be GREATER than 150 lbs

The way I did this is as follows:

P(X>150)

P((x-143)/29)>(150-143)/29))

I solved the one on the right and got.24137931, which is in relation to a z score. I have a chart for this, and I look up .24 and get a probability of .5948. I want everything on the other side right, so I subtract that from 1 and get.4052(or 41%) as my answer

Did I do it correctly? I have no way to check my work.

Women's Weight are normally distributed with a mean of 143 & a standard deviation of 29lb.

b) Find the probability that 12 randomly selected women will have a mean that will be GREATER than 150 lbs

This one is very confusing to me, and im not entirely sure where to start.

EDIT:

So after some thinking and searching i tried the following (still need someone to check it, as I have no way to myself)

to get the new standard deviation i did 29/12^(1/2) (square root of 12)

8.3715789, which I rounded up to 8.4

(150-143)/8.4 = 0.833333333

I look at my chart for .83 and get .7939

Then 1-.7939 to get .2061, or 21%

I appreciate all help that comes my way