Assuming that two independent random samples from machines A and B are selected, the sampling distribution of the difference in the sample proportions of defective parts has a mean of 0 and the distribution is approximately normal.
This statement is true based on the sample size of 100, which is large enough to support the truth for proportions according to the Central limit theorem.
It comprises a statistical result, which according to probability theory states that there is a relationship between the sample size and the sample distribution.
That is, when there is an increase in the sample size, the sample distribution of the mean tends to a normal distribution.
Therefore, it is correct to state that in a sample of size 100 randomly selected from machines A and B, which has a mean of 0, it will have a normal distribution, because there is a greater probability of an event close to the mean than in the extremes.
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