# Thread: I'm so lost.... normal distribution & standard deviation

1. ## I'm so lost.... normal distribution & standard deviation

Ok, so I give in. I have no clue how to do this. Can anybody help?? I would love a step-by-step explanation of how to find the answers....

The length of elephant pregnancies from conception to birth varies according to a distribution that is approx. normal with mean 525 days and standard deviation 32 days.

What % of pregnancies last more than 600 days?

What % of pregnancies last between 510 and 540 days?

How short do the shortest 10% of all pregnancies last?

2. Originally Posted by brittanyblair
Ok, so I give in. I have no clue how to do this. Can anybody help?? I would love a step-by-step explanation of how to find the answers....

The length of elephant pregnancies from conception to birth varies according to a distribution that is approx. normal with mean 525 days and standard deviation 32 days.

What % of pregnancies last more than 600 days?
In the problem, we're told that $\mu=525$ and $\sigma=32$

Let $X$ be the random variable that represents the length of an elephant's pregnancy.

Thus, we are to find $P\!\left(X>600\right)$.

To solve this problem, we must incorporate the $z$-score.

We know $z=\frac{x-\mu}{\sigma}$.

Thus, $P\!\left(X>600\right)=P\!\left(X-\mu>600-525\right)=P\!\left(\frac{X-\mu}{\sigma}>\frac{600-525}{32}\right)\approx P\!\left(Z>2.344\right)$

Now you can use the standard normal distribution tables to see that $P\!\left(Z>2.344\right)=1-\Phi\!\left(2.344\right)\approx\color{red}\boxed{. 0095}$ or 0.95%.

What % of pregnancies last between 510 and 540 days?
Using a similar idea, you can show that $P\!\left(510

I leave it for you to determine this value.

How short do the shortest 10% of all pregnancies last?

I'm not quite sure what to make of this part. Maybe someone else can help you with this.

I hope what I've helped with makes sense!

3. Thanks Chris. This did help. I appreciate you breaking down the steps - helps it make much more sense!

This makes me sound even dumber than I already do..... but that's life. For the 2nd problem (510 < X < 540).... how do I translate that into a percent?

I promise, I'm not "this bad" at math

Still hoping that someone is able to help with the last question....

4. Originally Posted by brittanyblair
Thanks Chris. This did help. I appreciate you breaking down the steps - helps it make much more sense!

This makes me sound even dumber than I already do..... but that's life. For the 2nd problem (510 < X < 540).... how do I translate that into a percent?

I promise, I'm not "this bad" at math

Still hoping that someone is able to help with the last question....
This thread contains most of the ideas and steps that you need to use: