# Gaussian distribution help!!

Tags:
1. Aug 25, 2016

• Member warned that an attempt must be shown
1. The problem statement, all variables and given/known data

I'm new to Gaussian and I've been on this problem for hours, I can't crack it at all (no pun intended) can anyone provide a detailed walk through the answers?

On average 5% of eggs contain a hereditary condition. Use Gaussian distribution to find the probability that

In a box of ten eggs none carry the hereditary condition
Batch of 500 there are 20 that carry the hereditary condition
In a batch of 10000 there are LESS than 1000 faulty!

2. Relevant equations
I can't use equation tool on this ancient phone

3. The attempt at a solution
Completely stumped

2. Aug 25, 2016

Some of the problem uses the binomial distribution. Parts of the problem are most easily calculated simply using the binomial without even approximating it by a Gaussian. The last part is most readily done by approximating the binomial to a Gaussian with same $\mu$ and $\sigma$. You should know that $\sigma$ for a binomial is $\sigma=\sqrt{Npq}$.

Last edited: Aug 25, 2016
3. Aug 25, 2016

### Ray Vickson

What, exactly, do you know about the Gaussian distribution? Where are you stuck?

Do you know what mean and variance represent? Do you know how to find the appropriate mean and variance in this problem? Do you know how to transform a problem with arbitrary mean and variance to an equivalent problem with mean = 0 and variance = 1? Do you know what needs to be done after that?

4. Aug 25, 2016

I need to find the variance and mean and standard deviation from the Gaussian distribution

5. Aug 25, 2016

### Ray Vickson

No, you don't. You have it backwards. You need to find the appropriate mean and variance; THEN you can figure out what is the correct Gaussian distribution for this problem.

6. Aug 25, 2016

How do I find that from the supplied data? Sorry I'm really stuck

7. Aug 26, 2016

### Staff: Mentor

Post #2 from @Charles Link is a very strong hint. The underlying distribution is a binomial distribution -- an egg either has the hereditary defect or it doesn't, and the problem here is to approximate this binomial distribution with a normal (or Gaussian) distribution. The p (= $\mu$) that Charles link mentions is pretty much given in the problem, and he has given an formula for finding $\sigma$.

8. Aug 26, 2016

Yes, I agree. One minor correction $\mu=Np$.

9. Aug 26, 2016

### Staff: Mentor

Right you are. I taught statistics a number of times, some years ago, but this one slipped my mind.