What is the Probability of Hereditary Conditions in a Gaussian Distribution?

[conrad dunk]

Homework Statement

Please help!

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 thatIn 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!

Homework Equations

I can't use equation tool on this ancient phone

The Attempt at a Solution

Completely stumped

 

[Charles Link]

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 $\sigma=\sqrt{Npq}$.

 

[Ray Vickson]

Homework Statement

Please help!

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 thatIn 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!

Homework Equations

I can't use equation tool on this ancient phone

The Attempt at a Solution

Completely stumped

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?

 

[conrad dunk]

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

 

[Ray Vickson]

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

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.

 

[conrad dunk]

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

 

[Mark44]

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

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 $\sigma$.

 

[Charles Link]

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 $\sigma$.

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

 

[Mark44]

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

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