From two machines that automatically pack coffee, samples of 64 bags have been extracted in each one of them. The probability distribution of the weight of each bag for both populations has identical means and standard deviations of 6.4 grams and 7.4 grams, respectively. Find the probability that the difference between the sample means exceeds 0.6 grams in absolute value. The exercise gives 0.6170 as a result, but I am interested in knowing how this result is reached? I hope you can help me. Now the difference of two independent normals $N(μ_1, σ_1)$ and $N (μ_2, σ_2)$ is a normal $N (μ_1 − μ_2, √σ^2_1 + σ^2_2)$
the difference between the sample means is a normal $Z∈N$ $(0, √6.4^2 + 7.4^2 / 8).$
For calculate P (| Z |> 0.6) I do the calculations and I don't understand why I don't get the result of 0.6170. please i need the help. I was parsing an answer and they removed it, so I couldn't follow up on the issue any further.
