# Math Help - Stats Questions: Probability and Normal Distributions

1. ## Stats Questions: Probability and Normal Distributions

3. The life of one species of poplar tree is normally distributed with mean 20 years and standard deviation 2.3 years.
(a) If one tree is selected at random, what is the probability that it will live 21 years or more?

I used Z = x - u/o to find a 67% probability

(b) If nine trees are selected at random, what is the probability that the sample mean life of the nine trees will be 21 years or more?

What formula do I need to use for this part? I am working on a bunch of take-home problems and my head is swimming afer 6 hours! Thanks!

2. Originally Posted by JeanetteR
3. The life of one species of poplar tree is normally distributed with mean 20 years and standard deviation 2.3 years.
(a) If one tree is selected at random, what is the probability that it will live 21 years or more?

I used Z = x - u/o to find a 67% probability

(b) If nine trees are selected at random, what is the probability that the sample mean life of the nine trees will be 21 years or more?

What formula do I need to use for this part? I am working on a bunch of take-home problems and my head is swimming afer 6 hours! Thanks!
Hi JeanetteR,

b)
Since it is a normal distribution. You can say the following:
$\mu_{\overline X} = \mu_X$
$\sigma_{\overline X} = \frac{\sigma_X}{\sqrt{n}}$

In this case you are taking a sample of n = 9.

3. Originally Posted by JeanetteR
3. The life of one species of poplar tree is normally distributed with mean 20 years and standard deviation 2.3 years.
(a) If one tree is selected at random, what is the probability that it will live 21 years or more?

I used Z = x - u/o to find a 67% probability Mr F says: Zounds! How can the probability of being greater than the mean (21 > 20) possibly be greater than 0.5 ....? You have found Pr(X < 21) methinks ....

(b) If nine trees are selected at random, what is the probability that the sample mean life of the nine trees will be 21 years or more?

What formula do I need to use for this part? I am working on a bunch of take-home problems and my head is swimming afer 6 hours! Thanks!
..

4. So I should take Z = x - u/o and subtract it from 1 to get the right probability then?

5. Originally Posted by JeanetteR
So I should take Z = x - u/o and subtract it from 1 to get the right probability then?
Draw a simple picture of the distribution and the area you require to see what you need to do.

6. So are you saying I should draw another curve, or should I just tape together the infinitely small bits of ripped note paper strewn on the floor with 15 bajillion other curves drawn on them?? I'm thinkin' the artistic side of retaping them may be therapeutic.

My P for part a is now 0.43 after redoing math. At least I think that was math.

Between two classes, I've been sitting here studying for 16 hours. I'd go home and go to bed, but I'm not sure I can remember where I live!

Youthinks I have found Pr(x<21). Methinks I am giving up for the night.

Thanks for the help... I'll probably have another q or two tomorrow!