Here is the problem:
Apples are being packed in a box. One apple weight is expected to be 200 g with a dispersion of 20 g.
Packing is stopped as soon as the total weight is 10 kg or more. Calculate the probability $$P(N≤49)$$ when $N$ is the number of apples in the box.
I assume that I have to use central limit theorem somehow. I have done similar exercises before but this one is a little bit different and I just can't get it started.
$X_i$ be the weight of $i$-th apple. $P(N\leq 49)=P(\sum_{i=1}^{49}X_i\geq 10000)=P(\bar X\geq 10000/49)=P(\sqrt{49}(\bar X-200)/20\geq \sqrt{49}(10000/49-200)/20)\approx\Phi(7(10000/49-200)/20)$
where $\Phi$ is the cdf of $N(0,1).$