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1. eggs are sold in boxes of 12. for each egg the probability that it is cracked is 0.05 independently of all other eggs. a randon sample of n boxes is selescted and the variance of the sample mean is 0.019 find the value of n??????????????????????????????? ??????????????????

thanks
2. We need the formula Var(aZ + b) = a^2 Var(Z), which works for any random variable Z and any numbers a and b.

--

Let X be the number of broken eggs in the sample.

X ~ Bin(12n, 0.05)
Var(X) = 12n*0.05*0.95 = 0.57n

Let Y = X/n be the number of broken eggs per box in the sample.

Var(Y) = Var(X)/n^2 = 0.57/n

[Var(Y) goes down as n increases.]

The question says that Var(Y) = 0.019. So n = 0.57/0.019 = 30.
3. (Original post by Jonny W)
We need the formula Var(aZ + b) = a^2 Var(Z), which works for any random variable Z and any numbers a and b.

--

Let X be the number of broken eggs in the sample.

X ~ Bin(12n, 0.05)
Var(X) = 12n*0.05*0.95 = 0.57n

Let Y = X/n be the number of broken eggs per box in the sample.

Var(Y) = Var(X)/n^2 = 0.57/n

[Var(Y) goes down as n increases.]

The question says that Var(Y) = 0.019. So n = 0.57/0.019 = 30.

im doin ocr s2 and ive never come across the formula
Var(aZ + b) = a^2 Var(Z), is it from s1 and i cant remember it or is there a different way?
4. Sorry, the formula comes from OCR S3 (it's in Edexcel S1).

You are meant to know however that

Var(sample mean) = sigma^2 / n

where sigma^2 is the variance of the distribution and n is the sample size.

In our case, sigma^2 = variance of number of broken eggs in a box = 12*0.05*0.95 = 0.57. So Var(sample mean) = 0.57/n.
5. (Original post by Jonny W)
Sorry, the formula comes from OCR S3 (it's in Edexcel S1).

You are meant to know however that

Var(sample mean) = sigma^2 / n

where sigma^2 is the variance of the distribution and n is the sample size.

In our case, sigma^2 = variance of number of broken eggs in a box = 12*0.05*0.95 = 0.57. So Var(sample mean) = 0.57/n.
thankyou i get it now!

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