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1. 30 apples are chosen at random their masses in x grams are summarised

signa x=3033

sigma x squared= 306676

find unbiased estimates of the mean and vairence of the mass of an apple in the box (i calculated mean=101.1g and variance=1.369g)

the apples are packed in boxes of 10 and the shopkeeper told customers most bags weigh more than a kilogram show that the shopkeepers statement is correct indicating any assuptions mad in your calculations

im stuck on the second part any help would be much appriciated!
2. Let X be the weight of a bag. We assume that:
(i) the weights of apples in a bag are independent of one another;
(ii) the mean and variance of the weight of an apple are 101.1 and 1.369.

Then by the central limit theorem we can approximate the distribution of X by N(1011, 13.69).

So

P(X >= 1000)
~ 1 - Phi(-11/sqrt(13.69))
= 0.9985
3. (Original post by Jonny W)
Let X be the weight of a bag. We assume that:
(i) the weights of apples in a bag are independent of one another;
(ii) the mean and variance of the weight of an apple are 101.1 and 1.369.

Then by the central limit theorem we can approximate the distribution of X by N(1011, 13.69).

So

P(X >= 1000)
~ 1 - Phi(-11/sqrt(13.69))
= 0.9985
thanks!

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